Question

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

Answer 1

a₁ = 37
a₂ = 74
d = a₂ - a₁ = 74 - 37 = 37

a(n) = 37 + 37(n-1)

Answer 2

Let us observe the given series 37,74,111,148

Here, the first term (a) = 37

Common difference(d) = 74-37 = 37

Hence, the given series is in Arithmetic progression.

Hence the nth term of the series is given by:

$a_{n}=a+(n-1)d$

Substituting the values of 'a' and 'd'.

$a_{n}=37+37(n-1)$

Therefore, it is the required explicit formula.