Question

if the nth term of an AP is (2n+1), find the sum of the first n terms of the AP​

Answer 1

Step-by-step explanation:

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) Ans.

Answer 2

Answer:

Sn = n/2 [2a+(n-1)d]

Step-by-step explanation:

Sn = 2n+1/2 [2a+(2n+1-1)d]

= 2n+1 /2 [2a+2nd]

= 2n+1/2 * 2[a+nd]

= 2n+1 [a+nd]

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