Sum of n terms of a certain series is given by S_n=2n+3n^2, what is the type of the series and what is its 20th term?

Baqling

Baqling

Answered question

2022-09-08

Sum of n terms of a certain series is given by S n = 2 n + 3 n 2 , what is the type of the series and what is its 20-th term?

Answer & Explanation

Raina Russo

Raina Russo

Beginner2022-09-09Added 20 answers

As sum of n terms of a certain series is given by S n = 2 n + 3 n 2

Sum of 20 terms is 2 × 20 + 3 × 20 2 = 40 + 1200 = 1240

Further, sum of 19 terms is 2 × 19 + 3 × 19 2 = 38 + 1083 = 1121 ,.
Hence 20th term is 1240−1121=119.

As sum of 1 term is 2 × 1 + 3 × 1 2 = 5 , sum of first two terms is 2 × 2 + 3 × 2 2 = 4 + 12 = 16 , second term is 16−5=11 and common difference is 11−5=6. If it is arithmetic progression the third term should be 11+6=17.

As sum of first three terms is 2 × 3 + 3 × 3 2 = 6 + 27 = 33 , third term is 33−16=17 hence it is an arithmetic progression.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?