Question

♠ QUESTION :

ANSWER MUST NOT BE COPIED.

Answer 1

Let the G.P of even number of terms be a ,ar ,ar^2 ,ar^3 , ar^4 .........2n.

as we know that sum of G.P

S n = a( r^n - 1 ) / r - 1 ___________eq.(1)

here, n = 2n , so now , put value of 'n' in eq. (1) , we get , the sum

S 2n = a (r^ 2n - 1 ) / r - 1________eq.(2)

let , a , ar^2 , ar^4 ....... to n is a required G.P of odd terms.

here , first term, = a

then common ratio = second term / first term

= ar^2 / a = r^2

now sum of series occupying odd places be

put value of 'a' and r = r^2 and n = 1 (odd)

in eq. (1) , we get

S1 = a ( r^2 )^n - 1 / (r^2 - 1 )

S1 = a ( r^2n - 1 )/ r^2 - 1._______eq.(3)

according to question ,

sum of all terms = 5 × sum of terms occupying odd places

S 2n = 5 × S 1

a (r^2n - 1 )/( r - 1 ) = 5 × a (r^2n - 1 )/r^2-1)

a (r^2n - 1 ) =5 × ( r - 1 ) a(r^2n - 1) /( r - 1 ) (r + 1 )

a ( r^2n - 1 ) / a ( r^2n - 1 ) = 5 /( r + 1 )

5 /( r + 1 ) = 1

5 = r + 1 => r = 5 - 1 = 4

therefore , common ratio = 4

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Your Answer : common ratio = 4
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