The number of terms of an A.P. is even; the sum of the odd terms is 24, and of the even terms is 30, and the last term exceeds the first by 21/2 then the number of terms in the series is 8`` b. 4`` c. 6`` d. 10

Options

A. 8
B. 4
C. 6
D. 10

Answer

D

Explanation

Given, `a_(1),a_(2),a_(3),..` are terms of A.P
`therefore(a_(1)+a_(2)+…+a_(p))/(a_(1)+a_(2)+…+a_(q))=(p^(2))/(q^(2))`
`rArr(p/2[2a_(1)+(p-1)d])/(q/2[2a_(1)+(q-1)d])=(p^(2))/(q^(2))`
or `(2a_(1)+(p-1)d)/(2a_(1)+(q-1)d)=p/q`
or `[2a_(1)+(p-1)d]q=[2a_(1)+(q-1)d]p`
or `2a_(1)(q-p)=d[(q-1)p-(p-1)q]`
or `2a_(1)(q-p)=d(q-p)`
or `2a_(1)=d`
`therefore(a_(6))/(a_(21))=(a_(1)+5d)/(a_(1)+20d)=(a_(1)+10a_(1))/(a_(1)+40a_(1))=11/41`