a1=28 and a13=100 find: a37

Question

arithmatic sequence maze

Answer 1

The formula for a term in an arithmetic sequence is:

a_n = a₁ + (n - 1)d

where a_n is the nth term, a₁ is the first term, n is the number of terms, and d is the common difference. The common difference is the amount that is added or subtracted from term to term.

In this problem, we are given the first term and the 13th term. So let’s use the 13th term to find the common difference, d.

a₁₃ = 28 + (13 - 1)d

100 = 28 + 12d

72 = 12d

d = 6

Now find the 37th term:

a₃₇ = 28 + (37 - 1)(6)

a₃₇ = 28 + (36)(6)

a₃₇ = 28 + 216

a₃₇ = 244