Why the common difference multiplied by the position of the term.

How to proved these numbers do not form an arithmetic progression (AP)

Find the formula for the nth term of an AP.

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# Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 1², 5², 7², 73, . . .

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1², 5², 7², 73, . .

a₂ – a₁ = 5² -1² = 25 – 1 = 24

a₃ – a₂ = 7² – 5² = 49 – 25 = 24

a₄ – a₃ = 73 – 7² = 73 – 49 = 24

The difference between the successive terms are same Hence, it is an A.P.

Common difference = 24, next three terms of this AP is as follows:

Fifth term a₅ = a₄ + d = 73 + 24 = 97

Sixth term a₆ = a₅ + d = 97 + 24 = 121

Seventh term a₇ = a₆ + d = 121 + 24 = 145