Question

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

• A. $10$
• B. $11$
• C. $12$
• D. None of these

Answer 1

The correct option is B $11$

Let $a$ be the first term and $d$ is the common difference of the A.P
Given sum of first four term of the A.P is 56,and first term is 11.
$\Rightarrow 11+(11+d)+(11+2d)+(11+3d)=56\Rightarrow 22+3d=28\Rightarrow d=2$
And sum of last four term is 112,
$\Rightarrow [11+(n-1\left)2\right]+[11+(n-2\left)2\right]+[11+(n-3\left)2\right]+[11+(n-4\left)2\right]=112$
$\Rightarrow 44+8n-10\times 2=112\Rightarrow n=11$