The first and last terms of an A.P. are 1 and 11.

Question:

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be

(a) 5

(b) 6

(c) 7

(d) 8

Solution:

In the given problem, we need to find the number of terms in an A.P. We are given,

First term (a) = 1

Last term (an) = 11

Sum of its terms 

Now, as we know,

$S_{n}=\left(\frac{n}{2}\right)(a+l)$

Where, a = the first term

l = the last term

So, we get,

$36=\left(\frac{n}{2}\right)(1+11)$

$36(2)=12 n$

$n=\frac{36(2)}{12}$

$n=6$

Therefore, the total number of terms in the given A.P. is $n=6$

Hence the correct option is (b).

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