Math, asked by Eduline2307, 10 months ago

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

Answers

Answered by Anonymous
20

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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