Advertisements
Advertisements
Question
Find the sum of G.P. :
0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.
Advertisements
Solution
Given G.P. : 0.3 + 0.03 + 0.003 + 0.003 + ...........
Here,
First term, a = 0.3
Common ratio, r = `0.03/0.3`= 0.1 ...(∵ r < 1)
Number of terms to be added, n = 8
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_8 = (0.3(1-(0.1)^8))/(1-0.1)`
= `(0.3(1 - (0.1)^8))/0.9`
=`(1 - (0.1)^8)/3`
= `1/3(1 - 1/10^8)`
RELATED QUESTIONS
Fourth and seventh terms of a G.P. are `1/18` and `-1/486` respectively. Find the G.P.
If the first and the third terms of a G.P. are 2 and 8 respectively, find its second term.
Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.
Find the third term from the end of the G.P.
`2/27, 2/9, 2/3, .........,162.`
Q 8
If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `1/x + 1/y = 2/b`
If a, b, c are in G.P. and a, x, b, y, c are in A.P., prove that `a/x + c/y = 2`
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Find the geometric mean between 14 and `7/32`
Q 7
