How i solve the problem of exercise 5.3 question no.5 .Please help me sir to solve this question in a easy way . The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

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# The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference. Q.5

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Given that,

first term, a= 5last term, l= 45Sum of the AP, S= 400_{n}As we know, the sum of AP formula is;

S=_{n}n/2 (a+l)400 =

n/2(5+45)400 =

n/2(50)Number of terms, n=16As we know, the last term of AP series can be written as;

l = a+(n−1)d45 = 5 +(16 −1)

d40 = 15

dCommon difference, d= 40/15 = 8/3