Q3 of 27 Page 79

The square of a term in the arithmetic sequence 2, 5, 8, …, is 2500. What is its position?

The square of a term is 2500.


⇒ Term = √2500 = 50


Given, arithmetic sequence 2, 5, 8 …


Here first term = 2 = a1


Common difference = 5 – 2 = 3 = d


We know that the expression on nth term in an arithmetic sequence is tn = a1 + (n – 1) d where n is the number of term.


⇒ 50 = 2 + (n – 1) (3)


⇒ 50 = 2 + 3n – 3


⇒ 50 = 3n – 1


⇒ 50 + 1 = 3n


⇒ 51 = 3n


⇒ n = 51/ 3


⇒ n = 17


∴ The position of the term 50 is 17.


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