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

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Question 1124668: How do I set up the problem for this information: Generate the first 3 terms of a sequence that obey the following recursive rules:
a0=4
an=an-1+2

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Question 1124731: the first term of an A.P is 7,the last term is 70 and sum is 385.find the number of terms in the series

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Question 1124908: the first three terms of geometric progression are x-2,x+1AND x+7. FIND THE VALUE OF X.THE COMMON RATIO. S6 . THE SUMMER TO INFINITY.
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Question 1124924: I need the next number in the sequence and why:
3, 3, 5, 4, 4, 3, 5, 5, 4, 3, _

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Question 1124931: 3 -6 12 4 20
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Question 1124987: The first and second terms of an arithmetic sequence are a and b respectively. If the nth term is c, express n in terms of a b and c and hence find the sum of these n terms.
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Question 1125134: f(n)=4*2(n-1)
I have to use the explicit formulas to generate the first 4 terms of each geometric sequence.

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Question 1125134: f(n)=4*2(n-1)
I have to use the explicit formulas to generate the first 4 terms of each geometric sequence.

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Question 1125133: what is the Nth term for these sequences
-1,0,3,8,15,24
-4,0,6,14,24,36

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Question 1125206: 51,04,81,38,03,25,23,51,23,49 what will be next number?
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Question 1125273: The sequence is missing 4 number, I need to know what’s the pattern to find the missing numbers...
2493, _, _, _, _, 8008

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Question 1125283: Find the rule for this table
S T
_ 70
_ 66
9 62
12 58
15 54

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Question 1125397: in a Gp if T3=12 and T6=96
Find the 10th term

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Question 1125702: What comes next -2,4,-8,16,....
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Question 1125757: The first term of an A.P is -2. If the ratio of 5th and 7th is 5:8, what is the common difference?
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Question 1125867: What is the next numbers in these sequences and why are they as they are:
-9 -8 -4 5 21 46 ... ...
and
2 4 6 10 16 26 42 ... ...
Thank you

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Question 1125867: What is the next numbers in these sequences and why are they as they are:
-9 -8 -4 5 21 46 ... ...
and
2 4 6 10 16 26 42 ... ...
Thank you

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Question 1125904: Suppose that the first term of a pattern is
3
. Each subsequent term is
8
more than the term before it.
Enter the first
6
terms of the pattern in the table below.( I need a table)

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Question 1125984: Given that x+6,x and x-3 are the first three terms of geometric progression.calculate the volume of x?.(i)find the value of x. (ii)the fifth term .(iii) the sum of infinity

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Question 1126169: Find the first term and the common difference of the arithmetic sequence whose
7th term is -30 and 12th term is -55.
first term
common difference

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Question 1126253: Is the sequence a[n]=6n-17 arithmetic?
if it is what is its first term
and its common difference

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Question 1126255: Find the common ratio and write out the first four terms of the geometric sequence
7^n+2/2?

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Question 1126362: Find the common ratio and write out the first four terms of the geometric sequence
9^n+3/10
a[1]=
a[2]=
a[3]=
a[4]=
common ratio ?

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Question 1126429: A right triangle has one vertex on a graph of y=√X at (x,y) another at the origin, and the third on the (positive) y-axis at (0,y). Express the area A of the triangle as a function of x. Sketch a picture

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Question 1126478: I need to know the next 3 numbers in the following pattern:
3,1,24,6,2,21,9,3,20,12,4,18,15,5

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Question 1126361: For the sequence a[n]=2(a[n-1]-2)and a[1]=5?
find
its first term
its second term
its third term
its fourth term
it fifth term?

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Question 1126513: Find the four arithmetic means between 12 and -13.

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Question 1126517: What are the next three terms of the following sequence?
- 2, - 1, - 1/2, -1/4

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Question 1126516: The following is a geometric sequence.
-5, 25, -125, 625

TRUE

FALSE

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Question 1126515: Find S10 for the series 2 + 7 + 12 + 17 +...
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Question 1126515: Find S10 for the series 2 + 7 + 12 + 17 +...
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Question 1126559: If 8,x,y and 27 are four consecutive terms of a G.P, find the value of x and y.
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Question 1126566: what is the next letter in the series ?
caxfbuictldroe

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Question 1126579: What is the continues pattern for these numbers. 3, -6, 12, 4, 20, ?
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Question 1126514: Find S15 for the series -1 + -3 + -5 + -7 +...
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Question 1126798: By using the expansion of (2+x)^4 and (2-x)^4, find the exact value of (2+√3)^4 + (2-√3)^4
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Question 1126799: Prove that (n 1)=(1 n-1)=n
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Question 1126795: a). In an AP, the first term -5 and the last term is 105. If the sum of these terms is 1550, how many terms are there in the AP?
b). The first three terms of a G.P are x+1, x+3 and x+8, and find
i) The value of x
ii) The common ratio
iii) The sum of the first 15 terms.

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Question 1127055: Write the first five terms of the sequence.
a n = n^2 + 2

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Question 1127021: Can you help, please
HALT
+ HALT
= THERE
Each letter in this addition problem stands for a different digit, but, for example, the H stand for the same digit. Find the value of THERE. Thank you

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Question 1127070: x,2x+1,11 are three consecutive terms of an arithmetic sequence. Calculate(i) x.(ii) the 30th term.
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Question 1127066: the third term of a geometric sequence is 4 and the sixth term is 32/27. find the nth term.
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Question 1127086: Tn=3r^n-1,where r>0 Is the nth term of a geometric sequence. If the third term is 48 determine r
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Question 1127086: Tn=3r^n-1,where r>0 Is the nth term of a geometric sequence. If the third term is 48 determine r
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Question 1127085: show that the general term of the sequence -2/5,1/0,4/15,7/20,0/25,...can be written as Tn =3n -5/5n
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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