Question

in a nth term of an AP is (2n+1) what is the sum of its first three terms?

Answer 1

n th term l = 2n+1 (given)-----(1)

If we put n=1,we get first term of an A.P.

Then first term a=2(1)+1

a=3;-----(2)

Now we can find out sum of first n terms using this formula

sum of n terms of an A.P.=n/2(a+l)

(Here a is first term of an A.P. and l is last or nth term of A.P.)

Values of a and l putting in the equation (3) from (2) and (1)

Sum of first n terms of an A.P.=n/2(3+2n+1)

=> n/2(2n+4)

=> n(n+2)

Finally, sum of first n terms of an A.P. is n(n+2) 

Answer 2

Answer:

Given :

nth term = 2 n + 1

= > a₁ = 2 + 1

=  3

= > a₂ = 4 + 1

= 5

d = a₂ - a₁

= > 5 - 3

= 2

Sₙ = n / 2 [ 2 a + ( n - 1 ) d ]

S₃ = 3 / 2 [ 6 + 2 × 2 ]

S₃ = 3 / 2 [ 10 ]

S₃ = 3 × 5

S₃ = 15 .

Therefore , sum of first three numbers is 15 .