51 + 52 + 53 + ……. + 70

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Solution

The given series is 51 + 52 + 53 + … + 70.

Here, first term = a + b = 51

Common difference = a = 52 − 51 = 1

⇒ 1 + b = 51

⇒ b = 50

Therefore,

⇒ 70 = n + 50

⇒ n = 70 − 50 = 20

We know that the sum of a specified number of the consecutive terms of an arithmetic sequence is half the product of the number of the terms with the sum of the first and the last term.

∴ Sum of its first 20 terms = … (1)

Here,

Putting the values in equation (1):

Sum of first 20 terms =

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