# Geometric

posted by .

1) The sum of last three terms of GP having n terms is 1024 time the sume of first 3 terms of GP. If 3rd term is 5. Find the last term.

2) The sum of the first eight terms of a GP is five times the sum of the first four terms. Find the common ratio.

• Geometric -

(1) ar^(n-1) + ar^(n-2) + ar^(n-3) = 1024 (a + ar + ar^2)
ar^(n-3) (1 + r + r^2) = 1024a (1 + r + r^2)
r^(n-3) = 1024

It is known that the third term is 5, so: ar^2 = 5

The last term will be:
ar^(n-1) = ar^2. r^(n-3) = 5 x 1024 = ? (You can finish the rest of it, right?)

(2) S8 = 5 S4
a(r^8 - 1)/(r-1) = 5a(r^4 - 1)/(r - 1)
(r^4 - 1)(r^4 + 1) = 5(r^4 - 1)
r^4 + 1 = 5
r^4 = 4
r = ±sqrt(2)

## Similar Questions

1. ### math

1) If the sum of the first n terms of a series is Sn where Sn=2n²-n, (a)prove that the series is an AP, stating the first term and the common difference; (b)find the sum of the terms from the 3rd to the 12th inclusive 2) In an AP …
2. ### Math

1) If the sum of the first n terms of a series is Sn where Sn=2n²-n, (a)prove that the series is an AP, stating the first term and the common difference; (b)find the sum of the terms from the 3rd to the 12th inclusive 2) In an AP …
3. ### Math

Sum of4th and the 6th terms of an a,p is 42 . While the sum of the 3rd and 9th terms of the same a.p is 52. Find the (a) first term (b)common difference (c) sum of the first ten terms of the progression. Solution
4. ### Maths

1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is …
5. ### Further mathematics

An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth …
6. ### arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term …
7. ### arithmetic

1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term …
8. ### math

in an arithmetic sequence the common difference is equal to 2.the first term is also the first term of a geometric sequence. the sum of the first 3 terms of an arithmetic sequence and the sum of the first 9 terms of an arithmetic sequence …
9. ### Math3c

1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find …
10. ### Maths

The sum of the last three terms of a G.P having n terms is 1024 times the sum of the first three terms of the progression. If the third term is 5, find the last term.

More Similar Questions