Advertisements
Advertisements
Question
For the following G.P.'s, find Sn: 3, 6, 12, 24, ...
Solution
3, 6, 12, 24, ...
Here, a = 3, r = `6/3` = 2 > 1
Sn = `("a"("r"^"n" - 1))/("r" - 1)`, for r > 1
∴ Sn = `(3(2^"n" - 1))/(2 - 1)`
∴ Sn = 3(2n – 1)
APPEARS IN
RELATED QUESTIONS
If for a sequence, tn = `(5^("n" - 3))/(2^("n" - 3)`, show that the sequence is a G. P. Find its first term and the common ratio.
For a G.P., if a = 2, r = `-2/3`, find S6.
For a G.P., if S5 = 1023, r = 4, find a.
For a G.P., if t4 = 16, t9 = 512, find S10.
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n – S2n) = (S2n – Sn)2.
If for a sequence `t_n = 5^(n-3) / 2^(n-3),` show that the sequence is a G.P.
Find its first term and the common ratio.
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n – S2n) = (S2n – Sn)2.
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively , then verify that Sn(S3n - S2n) = (S2n - Sn)2
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n - S2n) = (S2n - Sn)2.
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n - S2n) = ( S2n - Sn ) 2.
If for a sequence, `t_n = (5^(n-3)) / (2^(n-3))`, show that the sequence is a G.P. Find its first term and the common ratio.
If Sn, S2n, S3n are the sum of n, 2n, and 3n terms of a G.P. respectively, then verify that `S_n (S_(3n) - S_(2n)) = (S_(2n) - S_n)^2`.
If for a sequence, `t_n = 5^(n-3)/2^(n-3)`, show that the sequence is a G.P. Find its first term and the common ratio.
If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n - S2n) = (S2n - Sn)2.
If for a sequence, `t_n = 5^(n-3)/2^(n-3)`, show that the sequence is a G.P. Find its first term and the common ratio.
If Sn , S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn(S3n − S2n) = (S2n − Sn)2
If `S_n, S_(2n), S_(3n)` are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that `S_n(S_(3n) - S_(2n)) = (S_(2n) - S_n)^2`.
