Question

Which of the following options is the recursive formula for the sequence {2, 12, 22, 32...}?

A) f(1)=2, f(n)=f(n−1)+10 for n>1
B) f(1)=10, f(n)=f(n−1)+2 for n>1
C) f(n)=2+10(n−1)
D) f(n)=10+2(n−1)

Answer 1

The recursive formula for the sequence is A) f(1)=2, f(n)=f(n−1)+10 for n>1, as it shows each term is 10 more than the previous one starting from 2.

Step-by-step explanation:

The recursive formula for the sequence {2, 12, 22, 32...} is found by analyzing the pattern between consecutive terms. The first term is 2, and each subsequent term increases by 10. Option A, f(1)=2, f(n)=f(n−1)+10 for n>1, correctly describes this pattern since it starts with the initial term of 2 and adds 10 to the previous term for each next term (n > 1).