Question

Sum of n terms in an AP is 3n^2+5n...find the AP and the 15th term

Answer 1

AP : 8, 14, 20, 26,.....
15th term is 92

Answer 2

Answer:

15th term is 92.

Step-by-step explanation:

Question:

The sum of n terms of an AP is 3n^2+5n. Find the AP hence find its 15th term.

Solution:

Sn= 3n² + 5n

Sn-1 = 3(n-1)² + 5(n-1)

= 3(n²+1-2n) +5n-5

= 3n² + 3-6n + 5n-5

= 3n²-n-2

Now,

an=Sn-Sn-1=3n²+5n-(3n²-n-2)

= 6n + 2

It means,

AP is 8, 14, 20,..........

Now for a15

=> a + 14d

=> 8 + 14(6)

=> 8 + 84

=> 92

Therefore,

15th term is 92.