Advertisements
Advertisements
Question
For a G.P., if the sum of the first 3 terms is 125 and the sum of the next 3 terms is 27, find the value of r.
Solution
S3 = 125, S6 = 125 + 27 = 152
Sn = `"a"((1 - "r"^"n")/(1 - "r"))`
∴ S3 = `"a"((1 - "r"^3)/(1 - "r"))`
∴ 125 = `"a"((1 - "r"^3)/(1 - "r"))` ...(i)
Also, S6 = `"a"((1 - "r"^6)/(1 - "r"))`
∴ 152 = `"a"((1 - "r"^6)/(1 - "r"))` ...(ii)
Dividing (ii) by (i), we get
`152/125 = (1 - "r"^6)/(1 - "r"^3)`
∴ `152/125 = ((1 + "r"^3)(1 - "r"^3))/((1 - "r"^3)`
∴ 1 + r3 = `152/125`
∴ r3 = `152/125 - 1`
∴ r3 = `27/125`
∴ r3 = `(3/5)^3`
∴ r = `3/5`
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 = 3, Sn = 242, find n.
For a G.P., if t4 = 16, t9 = 512, find S10.
Find the sum to n terms: 8 + 88 + 888 + 8888 + …
Find the sum to n terms: 0.7 + 0.77 + 0.777 + ...
Find the nth terms of the sequences: 0.5, 0.55, 0.555, …
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. `
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.
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 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 for a sequence, `"t"_"n" = (5^"n"-3)/(2^"n"-3)`, show that sequence is a G.P.
Find its first term and the common ratio.
