if f(n)=f(n-1)+7 and f(1)=-18 then f(37)=?

step by step solution

Recall the Recursive formula for an arithmetic sequence:

The recursive formula for the nth term of an arithmetic sequence for which the first term is a1 and the common difference is d is given with:

a_n=a_{n-1}+d

and, it is given that:

f(n)=f(n-1)+7\implies d=7

Let f(1) represent the first term of the arithmetic sequence series:

It means,

f(1)=a_{1}=-18

Similarly,

 f(37)=a_{37}

nth Term of an Arithmetic Sequence:

The nth term of an arithmetic sequence with the first term a1 and the common difference d is given by:

a_n=a_1+(n-1)d

on substituting the values in the above equation:

a_{37}=-18+(37-1)7\implies a_{37}=234

Hence, the required value of f(37)=234

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