1966 AMC 12 Problem 18

Attempt Problem 18 of the 1966 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 1966 AMC 12 solutions, or check the answer key.

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18.

In a given arithmetic sequence the first term is

2,

the last term is

29,

and the sum of all the terms is

155.

The common difference is:

3

2

\dfrac{27}{19}

\dfrac{13}{9}

\dfrac{23}{38}

Use

155=\frac{n(2+29)}{2}

to find the number of terms

Then use

29=2+(n-1)d

The sum formula gives

155=\frac{31n}{2},

n=10.

Therefore

29=2+9d,

and

d=3.

Thus, the correct answer is A.

Problem 18 in other years