Answer :

Sum of n terms of an AP is given by,

where 'a' is first term of AP, n is the number of terms of AP and 'a_{n}' is last term of AP.

Given,

First term, a = 5

and last term, a_{n} = 45

Also, sum = 400

Putting the values in the formula, we get

⇒ 800 = 50n

⇒ n = 16

i.e. there are 16 terms in given AP.

Now the nth term of an AP is given by the formula,

a_{n}=a+(n-1)d

where, a is the first term, n is the number of terms, a_{n} is the nth term and d is the common difference.

45 = 5 + (16 - 1) x d

⇒15d = 40

Therefore, common difference of AP is 8/3

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