Question

The sum of the first four terms of an AP is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

• A. 10
• B. 11
• C. 12
• D. 13

Answer 1

The correct option is B 11

$a=11$

Sum of first four terms = 56

$\frac{4}{2}[2\times 11+(4-1\left)d\right]=56$

$22+3d=28$

$3d=6$

$d=2$

Sum of last four terms = 112

$a_n+a_{n-1}+a_{n-2}+a_{n-3}=112$

$\frac{4}{2}[a_n+a_{n-3}]=112$

$a_n+a_{n-3}=56$

$[11+(n-1)\times 2]+[11+(n-4)\times 2]=56$

$4n=44$

$n=11$

Hence, there are 11 terms in the AP.