Question

In an A.p the sum of
firest n-temes is. (5n^2/2)+(3n/2)
Find the 17th tom.​

Answer 1

Given: Sum of the first n-terms is 5n²/2 + 3n/2

To find: The 17th term of the A. P.

Solution:

Step 1. We find the sum of the first 17 terms.

Sum of the first 17 terms is

= 5 (17)²/2 + 3 (17)/2

= 5 (289)/2 + 51/2

= 1445/2 + 51/2

= 1496/2

= 748

Step 2. We find the sum of the first 16 terms.

Sum of the first 16 terms is

= 5 (16)²/2 + 3 (16)/2

= 5 (256)/2 + 48/2

= 640 + 24

= 664

Step 3. We find the 17th term now.

The 17th term of the A. P. is

= sum of the first 17 terms

- sum of the first 16 terms

= 748 - 664 = 84

Answer: The 17th term is 84.