For every n the sum S_n of n terms of an arithmetic progression is 2n+3n^2. The r th term is:

1965 AMC 12 Problem 20

Attempt Problem 20 of the 1965 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1965 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

20.

For every

n

the sum

S_n

n

terms of an arithmetic progression is

2n+3n^2.

The

r

th term is:

3r^2

3r^2+2r

6r-1

5r+5

6r+2

The

r

th term equals

S_r-S_{r-1}

Compute the difference of the two quadratic expressions

The

r

th term is the difference of consecutive partial sums. Substitution and simplification give

S_r-S_{r-1}=6r-1.

Therefore, the correct answer is C.