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.
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,
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
Therefore, common difference of AP is 8/3
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The sum of n termKC Sinha - Mathematics