Question

Find an explicit formula for the arithmetic sequence 37,74,111,148,...37,74,111,148,...37, comma, 74, comma, 111, comma, 148, comma, point, point, point.

Answer 1

Tn = 37n

Explanation:

Given the arithmetic sequence 37,74,111,148,...3

The explicit formula for the arithmetic sequence is expressed as;

Tn = a + (n-1)d

a is the first term = 37

n is the number of terms

d is the common difference

d = 74 - 37 = 111 - 74 = 37

Substitute the given values into the formula

Tn = 37 + (n-1)*37

Tn = 37 + 37n - 37

Tn = 37n

Hence the required explicit formula is Tn = 37n