Question

16. The first and last terms of an A.Pare 1 and 11.if the sum of its terms is 36 , then the
number of terms is.............
​

Answer 1

Given :-

Ist term of AP = 1

Last term of AP = 11

Sum of it's terms = 36

To Find :-

The number of terms in the given AP.

Solution :-

We have,

Ist term = a = 1

Last term = l = 11

Sum S = 36

${\sf{S\: =\: {\dfrac{n}{2}}\: (a\: +\: l)}}$

On inserting the values in the formula

We get ,

${\sf{36\: =\: {\dfrac{n}{2}}\: (1\: +\: 11)}}$

${\sf{\implies\: 36\: =\: {\dfrac{n}{2}}\: (1\: +\: 11)}}$

${\sf{\implies\: 36\: =\: {\dfrac{n}{2}}\: \times\: 12}}$

${\sf{\implies\: 36\: =\: 6n}}$

${\sf{\implies\: n\: =\: {\dfrac{36}{6}}}}$

${\sf{\implies\: n\: =\: 6}}$

Therefore,

Number of terms in the given AP is $\red{6}$.

Answer 2

Answer :-

Given :-

• Ist term of AP = 1

• Last term of AP = 11

• Sum of it's terms = 36

To Find :-

• The number of terms in the given AP.

Solution :-

We have,

• Ist term = a = 1

• Last term = l = 11

• Sum S = 36

$\: {\sf{S\: =\: {\dfrac{n}{2}}\: (a\: +\: l)}}$

On inserting the values in the formula

We get ,

$\: {\sf{36\: =\: {\dfrac{n}{2}}\: (1\: +\: 11)}}$

$\: {\sf{\implies\: 36\: =\: {\dfrac{n}{2}}\: (1\: +\: 11)}}$

$\: {\sf{\implies\: 36\: =\: {\dfrac{n}{2}}\: \times\: 12}}$

$\: {\sf{\implies\: 36\: =\: 6n}}$

$\: {\sf{\implies\: n\: =\: {\dfrac{36}{6}}}}$

$\: {\sf{\implies\: n\: =\: 6}}$

Therefore,

Number of terms in the given AP is 6