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 257497: when asked what is the next number, or what is the sequence, what and how do you figure it out

Click here to see answer by stanbon(57290)

Question 257916: In an arithmetic series the sum of the first 9 terms is 162 and the sum of the first 12 terms is 288. Determine the series.
Click here to see answer by Theo(3458)

Question 258336: In an arithmetic sequence of positive numbers, the common difference is twice the first term, and the sum of the first six terms is equal to the square of the first term. Find the first term of the sequence.

Click here to see answer by palanisamy(496)

Question 258505: How do you get the sum 10 with the numbers; 2, 4, 9, and 3?

Click here to see answer by checkley77(12569)

Question 258505: How do you get the sum 10 with the numbers; 2, 4, 9, and 3?

Click here to see answer by richwmiller(9135)

Question 258570: How do I write a formula for M in terms of t?
This is the chart I'm given:
number of triangles (t) number of sticks (m) (making a pattern of triangles
1 (one) 6 (six)
2 (two) 10 (ten)
3 (three)
4 (four)
5 (five)
oops...the 6 and the 10 are supposed to appear under the column no.of sticks (m)
I just need a model answer so I can understand how to approach other ones. Any help would be really apprectiated.
Click here to see answer by drk(1908)

Question 258718: Write the explicit formula for the geometric sequence.
0.5,-0.1,0.02,-0.004, ...
Click here to see answer by vksarvepalli(154)

Question 258765: The sum of the first n terms in a sequence is always 1/n. Find the product of the first 2007 terms.

Click here to see answer by stanbon(57290)

Question 258681: three numbers are in AP and their sum is 21. if 1,5,15 are added to them respectively,they form a GP.The numbers are.
please tell me the solution and method of solving this type of questions.

the above is question of AP and GP.
Please reply me on email-id:- fernsnadia@gmail.com
Awaiting for yours earliest reply
Nadia Fernandes.
Click here to see answer by Fombitz(13828)

Question 259021: find 2 numbers thats sum is 28 and a product of 147
Click here to see answer by richwmiller(9135)

Question 259021: find 2 numbers thats sum is 28 and a product of 147
Click here to see answer by drk(1908)

Question 259612: Write the geometric series -9/2 + 3/2 - 1/2 + 1/6- ... + 1/39366 in summation notation
Anyone?
(:
Click here to see answer by scott8148(6628)

Question 259657: three numbers are in AP and their sum is 21. if 1,5,15 are added to them respectively,they form a GP.The numbers are.
please tell me the solution and method of solving this type of questions using this formula for Ap:(a-d),a, (a+d) and for GP:a/r,a,ar
the option for the above question is :A)5,7,9 B)9,7,5 C) none of these

the above is question of AP and GP.

Click here to see answer by Fombitz(13828)

Question 259658: three numbers are in AP and their sum is 21. if 1,5,15 are added to them respectively,they form a GP.The numbers are.
please tell me the solution and method of solving this type of questions using this formula for Ap:(a-d),a, (a+d) and for GP:a/r,a,ar
the option for the above question is :A)5,7,9 B)9,7,5 C) none of these
the above is question of AP and GP.

Click here to see answer by Fombitz(13828)

Question 259680: The first term in the sequence is 256. After the first term, each term is multiplied by two and then divided by four. What is the value of the 9th term?
(A) 8 (B) 4 (C) 2 (D) 1 (E) 0

Click here to see answer by Edwin McCravy(8904)

Question 259695: how do we get the expression (n+1)^2-3^(n+1)

Click here to see answer by Alan3354(30993)

Question 260663: A sequence begins with 1, 4, 7, … Another sequence begins with
99, 95, 91, … At which position is the positive difference between
the respective terms of the two sequences the minimum?

Click here to see answer by jsmallt9(3296)

Question 260678: Find the missing numbers in the sequence: 4, 10, 22, 46, _____, _____, 382
Click here to see answer by Fombitz(13828)

Question 260678: Find the missing numbers in the sequence: 4, 10, 22, 46, _____, _____, 382
Click here to see answer by PRMath(123)

Question 260678: Find the missing numbers in the sequence: 4, 10, 22, 46, _____, _____, 382
Click here to see answer by ankor@dixie-net.com(15647)

Question 261486: What is the formula for the nth term for the infinite sequence:
1,5,9,13,17,21,...
Click here to see answer by palanisamy(496)

Question 261707: Finish the following sequence: 5, 9, 21, 57, 165, ____, ____
Click here to see answer by Edwin McCravy(8904)

Question 261800: 4,5,9,18,34,59...........whts after 59
Click here to see answer by williamson.family05(2)

Question 262650: I can't seem to figure out where to begin, I keep getting incorrect answers. Could someone help please?
What are the missing terms of the arithmetic sequence -8,___, ___, 3?
What is Sn for the arithmetic series with a1 = 3, an = -38, and n = 8?
What is Sn for the arithmetic series with d = -4, an = 27, and n = 9?
Click here to see answer by edjones(7569)

Question 263151: The speed of light in a vacuum is 2.9979246 x E8 metres per second. Write this value to the following number of significant figures
a) 1
b) 3
c) 5
Thank you very much
Click here to see answer by drk(1908)

Question 263298: What is the 6th term of the followings sequence?
1 cube, 4cubes, 10 cubes
Click here to see answer by masoax(2)

Question 263488: How do you describe the pattern, write the next term and write the rule for the nth term for the sequences 1, 2, 4, 8,...
Click here to see answer by oberobic(2304)

Question 264758: 3+6+9+...+996+999=
1+3+3^2+3^3+...+3^30=
1+(-1)+(-1)^2+...+(-1)^1000=
Click here to see answer by stanbon(57290)

Question 264927: The sum of three consecutive natural numbers 1s 75. Find the three numbers.
Click here to see answer by josmiceli(9668)

Question 265252: Find "k" so when x^3 + kx^2 - kx + 1 is divided by x-2, the remainder is 0.
Click here to see answer by drk(1908)

Question 265498: What are the next two terms in each sequence?
1.3, 2.4, 3.5, 4.6, …
Click here to see answer by rfer(12657)

Question 265521: The sum of two numbers is less than or equal to 23 . The second number is 7 less than the first. What are the possible values for the first of the two numbers? I cannot come up with an answer for this one and I am getting frustrated can someone please help me, thank you.
Click here to see answer by roseo(33)

Question 265912: The nth term of a sequence is given by the formula n^2+2n How much larger is the 10th term of the sequence than the 9th term?

Click here to see answer by asuar010(324)

Question 265850: you want a sum of about 60. which 2 numbers would you add? 28/ 47/ 59/ 8
Click here to see answer by asuar010(324)

Question 265723: arithmetic sequence a10=x+3 a11=2x+7 a12=4x-2 which term equals 186
Click here to see answer by drk(1908)

Question 266257: Is 5,9,13,17,21
arithmeic or geometric sequence and what is the number that makes them go to the next number.
Click here to see answer by asuar010(324)

Question 266261: is 1,0.3,0.009,0.0027,0.0081 a geometric sequence or a arithmetic and what number is multiplied to get to the next

Click here to see answer by Alan3354(30993)

Question 266760: If someone could please help me with this problem, it would be greatly appreciated!
I have to find the sum of the geometric sequence
, , ...
This is what I have so far:
r=(1/3)

(it's supposed to be (n-1))
from this I got n=5

As elementary as this is, I need help finding the sum and understanding the process(es) of how to work this equation when fractions are in the mix. (That is, unless I've made mistakes prior to getting to this point.)

Click here to see answer by Edwin McCravy(8904)

Question 266763: Please help me solve this Geometric Sequence.
My teacher doesn't teach very well so it's kind of hard to comprehend everything.
equation-91st term: 1/5,-1/5,1/5,-1/5,1/5,...
Click here to see answer by drk(1908)

Question 267464: find the first six terms of arithmetic sequence
Click here to see answer by Edwin McCravy(8904)

Question 267871: Prove by mathematical induction: ∑_(i=1)^n (3^i= 3(3^n-1)/2)
Click here to see answer by Edwin McCravy(8904)

Question 268975: (2r^(-1)+s^(-1) )^5 Expand the Binomial.
Click here to see answer by persian52(158)

Question 268983: Insert K arithmetic means betweens the given numbers.
11/3 and 6; k=4
Click here to see answer by stanbon(57290)

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