Question

If the sum to n terms of a sequence be n2 + 2n, then prove that the sequence is an A.P.

Answer 1

Step-by-step explanation:

since, sum of nth term = n²+2n

first term= 1²+2×1= 3

sum of first two terms = 2²+2×2= 8

second term= 8-3= 5

sum of 1st, 2nd and 3rd term= 3²+2×3= 15

third term= sum of 3- sum of 2

= 15-8 = 7

thus sequence is

3, 5, 7, 9,,..........................2n+1

therefore sequence is an AP

Answer 2

Answer:

answer is This sequence is an AP.

( Hence Proved )

Step-by-step explanation:

We have Given that ,

Sum of nth term = n²+2n

First term = n² +2n

→ 1²+2×1= 3

Sum of first two terms = 2²+2×2= 8

Second term = 8 - 3=5

Sum of 1st , 2nd and 3rd term = 15

Third term = 15 - 8 = 7

Common Difference = 5-3 = 2

A.P. = 3,5,7,9,11 .......................2n+1

. ' . Sequence is an A.P.