Find the 37th term of the sequence 2, 5, 8, 11, 14, . . .

Solution:

An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same. 

Given, the sequence is 2, 5, 8, 11, 14,.....

We have to find the 37^th term of the sequence.

The given sequence is in arithmetic progression.

The n-th term of an arithmetic sequence is given by

a_n=a+(n-1)d

Here, first term, a = 2

Common difference, d = 5 - 2 = 3

a₃₇=2+(37-1)×3

= 2 + 36 × 3

a₃₇=110

Therefore, the 37th term is a₃₇=110

Find the 37th term of the sequence 2, 5, 8, 11, 14, . . .

Summary:

The 37th term of the sequence 2, 5, 8, 11, 14, . . .is a₃₇=110