Question

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

Answer 1

Answer:

The square of a term is 2500. 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. ∴ The position of the term 50 is 17.

Answer 2

Step-by-step explanation:

Given :-

2,5,8,...

To find :-

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

Solution :-

Given AP is 2,5,8,..

First term = (a) = 2

Common difference= (d) = 5-2 = 3

We know that

nth term of an AP = an = a+(n-1)d

We have

The square of a term = 2500

Let the square of nth term be 2500

=>( an )² = 2500

=> an = √2500

=> an = 50

=> a+(n-1)d = 50

=> 2+(n-1)(3) = 50

=> 2+3n-3 = 50

=> 3n-1 = 50

=> 3n = 50+1

=> 3n = 51

=> n = 51/3

=> n = 17

Therefore, 17 th term of the AP is 50

The square of 17th term is 2500

Answer :-

The square of 17th term is 2500 in the given AP .

Used formulae:-

nth term of an AP = an = a+(n-1)d

a = First term

d = Common difference

n = Number of terms