The first term of

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

⇒d = 40/15  

Therefore, common difference of AP is 8/3