Question

The first and last terms of an A.P of n terms is 1, 31 respectively. The ratio of $8^{th}$ term and $(n-2{)}^{th}$ term is 5:9, the value of n is:

• A. 14
• B. 15
• C. 16
• D. 13

Answer 1

The correct option is C 16

$31=1+(x-1)d$
$(x-1)d=30$...(A)
ratio given as $\frac{8^{th}term}{(n-2{)}^{th}term}=\frac{5}{9}$
$\frac{1+7d}{1+(x-3)d}=\frac{5}{9}$
from (A) $\frac{1+7d}{31-2d}=\frac{5}{9}$
$\therefore d=2$
from (A)
$(x-1)\times 2=30$
$x-1=15$
$x=16$