Advertisements
Advertisements
Question
Find the sum of G.P. :
`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.
Advertisements
Solution
Given G.P. : `1 - 1/2 + 1/4 - 1/8 + ..........`
Here,
First term, a = 1
Common ratio, r = `(-1/2)/1 = -1/2` ...(∵ r < 1)
Number of terms to be added, n = 9
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_8 = (1(1 - (-1/2)^9))/(1 - (-1/2))`
= `(1 - (-1/2)^9)/(1 + 1/2)`
= `(1 + 1/2^9)/(3/2)`
= `2/3(1 + 1/2^9)`
= `2/3(1 + 1/512)`
= `2/3 xx 513/512`
= `171/256`
RELATED QUESTIONS
Find the 9th term of the series :
1, 4, 16, 64, ...............
The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.
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.`
For the G.P. `1/27, 1/9, 1/3, ........., 81`; find the product of fourth term from the beginning and the fourth term from the end.
Find the sum of G.P. :
1 + 3 + 9 + 27 + .......... to 12 terms.
Find the sum of G.P. :
`1 - 1/3 + 1/3^2 - 1/3^3 + .........` to n terms.
Q 3.1
Q 3.3
The sum of three numbers in G.P. is `39/10` and their product is 1. Find the numbers.
