How many terms are in the finite arithmetic sequence 12, 20, 28, … , 172?

Expert Solution

Consider the finite arithmetic sequence,

12, 20, 28, … 172

Use the explicit formula for an arithmetic sequence,

an = a1 + (n – 1)d ...... (1)

First term of the sequence is a1 = 12

Compute common difference as follows:

d = a2 – a1

= 20 – 12

= 8

Substitute a1 = 12, an = 172 and d = 8 in the formula (1) an = a1 – (n – 1)d and simplify,

172 = 12 + (n – 1)8

8(n – 1) = 160

n – 1 = 20

n = 21

Therefore, there are 21 terms in the given arithmetic sequence.

Umair answered 1 year ago

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