Question

the first term and the last term of an ap are 5 and 45 respectively if the sum of all its term is 400 find it'd common different

Answer 1

SOLUTION:-

Given:

•The first term & the last term of an A.P. are 5 & 45 respectively.

•The sum of all term is 400.

To find:

The common difference.

Explanation:

We know that, formula of the sum of last term;

${}^{S} n = \frac{n}{2} (a + l)$

•First term,(a)= 5

•Last term,(l)= 45

•Sn= 400

According to the question:

$= > 400 = \frac{n}{2} (5 + 45) \\ \\ = > 400 = \frac{n}{2} \times 50 \\ \\ = > 800 = 50n \\ \\ = > n = \frac{800}{50} \\ \\ = > n = 16$

So,

The number of terms is 16.

Now,

The formula use is, Sn=n/2(2a+n-1)d

$= > 400 = \frac{16}{2} (2 \times 5 + (16 - 1) \times d) \\ \\ = >400 = 8(10 + 15d) \\ \\ = > \frac{400}{8} = 10 + 15d \\ \\ = > 50 = 10 + 15d \\ \\ = > 15d = 50 - 10 \\ \\ = > 15d = 40 \\ \\ = > d = \frac{40}{15} \\ \\ = > d = \frac{8}{ 3}$

Thus,

The common difference is 8/3.

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