Q. 54.4( 220 Votes )

The first term of

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 'an' is last term of AP.

Given, 
First term, a = 5
and last term, an = 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,

an=a+(n-1)d

where, a is the first term, n is the number of terms, an 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

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