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The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then the common difference is[[1]].

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Detailed Solution

The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then the common difference is 10.
Given, the first term

a = − 5

, last term

a n = 45

and sum of the terms

S n = 120

.
Another formula for sum of an A.P series, to obtain the number of terms

n

S n = n 2 a + a n

120 = n 2 − 5 + 45 120 = n 2 40 n = 24040 n = 6

So, Let’s find common difference

d

. Substitute -5 for

a

and 45 for

a n

and 6 for

n

a n = a + n − 1 d

to obtain the common difference

d

a n = a + n − 1 d 45 = − 5 + 6 − 1 d 50 = 5 d d = 10

So, the final answer is d = 10.

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