Question

The first term of an AP is 11. The sum of its first four terms is 56, and its last four terms is 112. Find the number of terms in the A.P. [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks

Let there be n terms in the AP, let d be the common difference, and let the last term be l. We have:

$l=11+(n-1)d$

Now, the sum of the first four terms will be:

$S_{firstfour}=\frac{4}{2}(22+3d)=56$

$\Rightarrow d=2$

And the sum of the last four terms will be:

$S_{lastfour}=\frac{4}{2}(2l-3d)=112$

$\Rightarrow 2l-3d=56$

$\Rightarrow l=31$

Using the values of l and d in the first relation, we have n = 11.