Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

Tutors Answer Your Questions about Sequences-and-series (FREE)

Question 1031545: A sequence is a function with domain the natural numbers 1,2,3,.... Using function notation, you can write the sequence an= a1+(n-1)d as an=a1+(n-1)d and the sequence an=a1r^n-1 as a(n)=a1r^n-1
a. s a(n)=a1+(n-1)d a linear function ? Explain, if not how can you adjust its definition so that it is a linear function ? What is the slope?
b.what type of function does an=a1r^n-1 suggest? To what family of functions does this function belong? explain how its related to the parent function os that family. Draw that graph.
c. what type of function is suggested by the sum sequence sn=a1(1-r^n)/1-r ?By sn= n/2 (a1 + a(n))? explan each answer
Click here to see answer by stanbon(75887)

Question 1031644: Use the first five terms of the trigonometric series (shown below) to approximate sin(π/5).
sin(x)=x-x^3/3!+x^5/5!-x^7/7!+...
Click here to see answer by Alan3354(69443)

Question 1031696: What is the recursive rule for the sequence: -7.4, -21.2, -35, -48.8, -62.2,...?
Thanks!
Click here to see answer by fractalier(6550)

Question 1031966: what is the similarity between numbers 85,17,19,4 and 2
Click here to see answer by Alan3354(69443)

Question 1032005: A (n)=0.5*3^n-1. I need to find the first fourth and eighth term. If you explain in simplest terms I would be super greatful
Click here to see answer by solver91311(24713)

Question 1032005: A (n)=0.5*3^n-1. I need to find the first fourth and eighth term. If you explain in simplest terms I would be super greatful
Click here to see answer by Boreal(15235)

Question 1031947: a company gives its employees a 4% raise at the beginning of every year.This year Jordan earns $32000. Write a rule to find Jordan's salary after n years?
Also, how many years will it take Jordan to earn $40,000?
Click here to see answer by Boreal(15235)

Question 1032025: What is the nth term of
4 4 0 -8 -20??

I was also given that the nth term of
2 2 0 -4 -10
Is 3n-n2 (n squared)

Click here to see answer by fractalier(6550)

Question 1032025: What is the nth term of
4 4 0 -8 -20??

I was also given that the nth term of
2 2 0 -4 -10
Is 3n-n2 (n squared)

Click here to see answer by stanbon(75887)

Question 1032051: given the geometric sequence: 18, 108/17,648/289,...
Find an explicit formula for a^n, where the first term is a^1=18
a^n=?
find a^11?
Click here to see answer by robertb(5830)

Question 1032224: Find the sum of first 35 terms of the series whose pth term is p/7+2.

Click here to see answer by stanbon(75887)

Question 1032225: Find the sum of first 35 terms o.
find the number of all interger between 100&800 each of which on division by 16 leaves the remainder 7.
Click here to see answer by ikleyn(52788)

Question 1032353: aadfjjjmmn?? What comes next series
Click here to see answer by Edwin McCravy(20056)

Question 1032441: Determine the next two numbers in the given sequence: 43, 44, 50, 53, 65, 70, 88, 95, 119...
Click here to see answer by jorel555(1290)

Question 1032441: Determine the next two numbers in the given sequence: 43, 44, 50, 53, 65, 70, 88, 95, 119...
Click here to see answer by Edwin McCravy(20056)

Question 1032522: Hi, these questions are really confusing, could you please help me?
For problems 9 and 10, write each sum using summation notation.
9.2 + 5 + 8 + 11 + ... + 29

10. 6 - 12 + 24 - 48 + ...

11. Find the sum of the arithmetic sequence 2, 4, 6, 8, ..., 70.

12. Find the sum of the geometric sequence
42,7,7/6,...,42,(1/6)^8

For problems 13 and 14, find the sum of the first n terms of the sequence. The sequences are either arithmetic or geometric.
13. -1, 11, -121, ...; n = 9

14. 14, 8, 2,...; n=9

15. Determine whether the infinite series is equal to a real number. If so, find the sum.

Click here to see answer by ikleyn(52788)

Question 1032559: A disease spread to infect fewer people over time. The total number of people infected was modeled by the following geometric series. 100+60+36+108/5+324/25+... What is the total number of people infected in the outbreak?
Click here to see answer by fractalier(6550)

Question 1032588: first four terms in the sequence -3(n+4)
Click here to see answer by fractalier(6550)

Question 1032803: Find a1 if s15= 2000 and r= 3.
Click here to see answer by Boreal(15235)

Question 1032819: given the set (-3,5), (5,7), (4,9) what is the domain and range of the data set?
Click here to see answer by Edwin McCravy(20056)

Question 1032830: A disease spread to infect fewer people over time. The total number of people infected was modeled by the following geometric series: 100+60+36+108/5+324/25+... What is the total number of people infected in the outbreak?

I know that each number is decreasing by 3/5 of the previous number but I couldnt get an even number of people.
Click here to see answer by fractalier(6550)

Question 1032812: Find a1 if Sn=468, an=375, and r=5.
Click here to see answer by fractalier(6550)

Question 1032853: Determine the type of series, then find the sum
1+4+7+10+......+43
Click here to see answer by fractalier(6550)

Question 1032941: What is the similarity among the numbers 85,17,19,4,2
Click here to see answer by ikleyn(52788)

Question 1032908: Find the missing term
a8 for {-1/250, -1/50, -1/10...}
Click here to see answer by robertb(5830)

Question 1032907: sequence
a1=8, r=1/2, n=9
Click here to see answer by fractalier(6550)

Question 1032906: Find S30: {50,45,40,35...}
Click here to see answer by ikleyn(52788)

Question 1033115: Find the nth term of the arithmetic sequence -8,-5,-2,1,4...

Click here to see answer by mananth(16946)

Question 1033128: y=(-1/2)x^2-6 was the result of shifting down 5 units, what was the original function?
Click here to see answer by Theo(13342)

Question 1033240: 7,21,8,72,9,

Click here to see answer by Edwin McCravy(20056)

Question 1033239: 2,7,26,101,400,?
Click here to see answer by Boreal(15235)

Question 1033237: 2,7,26,101,400,?
Click here to see answer by ikleyn(52788)

Question 1033283: If logk = c logv + logp , what does k equal?

Click here to see answer by Theo(13342)

Question 1033285: What does x equal in the following equation?
log4(x^2 - 4) - log4(x+2)= 2
Click here to see answer by ikleyn(52788)

Question 1033284: What does x equal in the following equations?
Solve for x.
3 ^(x^2 + 4x) = 3^(-4)
Solve for x.
4 ^(2x)=2^(3x + 2)
Solve for x.
8 ^ (2x) = 2 ^(2x + 8)
Click here to see answer by ikleyn(52788)

Question 1033282: What is the binomial expansion of (2x - 1)^5 as a polynomial in simplest form?
Click here to see answer by Edwin McCravy(20056)

Question 1033214: the number of terms in the following arithmetic sequence...
3a-5, a+1, 7-a,..., 109-35a

Click here to see answer by mananth(16946)

Question 1033339: Which number term of the sequence 5,10,15 is 275?
Click here to see answer by Fombitz(32388)

Question 963078: What number comes next in this number sequence?
1 2 8 48 384
Click here to see answer by xshofi(1)

Question 1033337: How do I find the 10th term of the sequence -6,1,-8?
Click here to see answer by ikleyn(52788)

Question 1033286: 2. The expression log(3+x) is undefined for what values of x?
3. If loga = (1/3)logx - 3logy, what is the value of a?
4. If loga=h and logb=j, write the expression log(a^3/b^2) in terms of h and j.
5. If log3=s and log2=t, rewrite the expression log72 in terms of s and t.
Click here to see answer by robertb(5830)

Question 1033412: 50 less than three times a number is equal to the number. What is the number?
Click here to see answer by ikleyn(52788)

Question 1033479: Safe�Driving Taxi Service charges $5 per pickup and $0.25 per mile. We�ll Get You There Cabs charges $1
per pickup and $0.50 per mile. At how many miles will the two companies charge you the same amount?

Click here to see answer by rfer(16322)

Question 1033525: Find the sum, if it exists.
32+16+8+...

Click here to see answer by jim_thompson5910(35256)

Question 1033663: Bag A contains 15 marbles of which 8 are red and the rest are black. Bag B contains 14 marbles of which 4 are red 3 are blue and the rest are black. A ball is drawn at random first from bad A, and second from bag B. If we make the random variable be black marbles (B) complete the following.
A) Create a tree diagram:
B) complete a probability table for the number of black marbles
Click here to see answer by Boreal(15235)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790