Question

Which term of the G.P.:

`-10, 5/sqrt(3), -5/6,....` is `-5/72`?

Answer 1

For the given G.P. :

First term, a = –10

Common ratio, r = `(5/sqrt(3))/(-10) = -1/(2sqrt(3))`

If `-5/72` is the n^th term of the given G.P., then `-5/(72)` = ar^{n – 1}

`\implies -5/72 = -10 xx (1/(2sqrt(3)))^(n - 1)`

`\implies 1/144 = (1/(2sqrt(3)))^(n - 1)`

`\implies 1/(2 xx 2 xx 2 xx 2 xx sqrt(3) xx sqrt(3) xx sqrt(3) xx sqrt(3)) =(1/(2sqrt3))^(n - 1)`

`\implies (1/(2sqrt3))^4=(1/(2sqrt3))^("n"-1)`

`\implies` n – 1 = 4

`\implies` n = 4 + 1

`\implies` n = 5