2015 AMC 10A Problem 7

Question

How many terms are in the arithmetic sequence

13,

16,

19,

\dotsc,

70,

73?

20

21

24

60

61

Use the first term, last term, and common difference

Count intervals, then add one endpoint

Recall that the

n

th term of an arithmetic sequence is

a + d(n - 1),

where

a

is the first term and

d

is the common difference.

For us,

a = 13

and

d = 3.

Plugging these in, we get that

\begin{aligned} 73 &= 13 + 3(n - 1) \\ 20&= n - 1 \\ n &= 21. \end{aligned}

Thus, B is the correct answer.

Problem 7 in other years