
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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