## The first term of an AP is 10, the last term is 105 and the sum is 1150. Find the number of terms and the common difference.

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## Answers ( )

a = 10

l = 105

2300 = n(115)

n = 20

n = 20

l = 105

a = 10

Hence the common difference is 5 and number of terms is 20.n = 20

a = 10

d = 5

HENCE VERIFIED.Given ,First term (a) = 10

nth term (an) = 105

Sum of first n terms (Sn) = 1150

We know that ,the sum of first n terms of an AP is given byThus ,1150 = n/2 × (10 + 105)

2300 = 115n

n = 2300/115

n = 20

Since ,nth term (an) = 105Thus ,105 = 10 + (20 – 1)d

95 = 19d

d = 95/19

d = 5

Therefore ,