Question

The number of terms in an $A.P$. is even; the sum of the odd terms in it is $24$ and that the even terms is $30$. If the last term exceeds the first term by $10\frac{1}{2},$ then the number of terms in the $A.P$. is :

• A. 4
• B. 8
• C. 12
• D. 16

Answer 1

Answer: (B)

Let no. of terms $=2n$
$a,(a+d),(a+2d)$, ,........ $a+(2n-1)d$
sum of even terms
$\frac{n}{2}[2(a+d)+(n-1)2d]=30......(i)$
sum of odd terms
$\frac{n}{2}[2a+(n-1)2d]=24.......(ii)$
$a+(2n-1)d-a=\frac{21}{2}......(iii)$
eq. (i)....eq. (ii)
$\frac{n}{2}\times 2d=6$
$\Rightarrow nd=6......(iv)$
$(2n-1)d=\frac{21}{2}......(v)$
$\frac{eq(iv)}{eq(v)}=\frac{n}{2n-1}=\frac{4}{7}$
$\Rightarrow 8n-4=7n$
$n=4$
so no. of terms $=8$