Question

A sequence is defined recursively by the formula f(n+1)=f(n)+3. The first term of the sequence is -4 what is the next term in the sequence ?

-7
-1
1
7

Answer 1

The next term is -1

Explanation:

`\left\{\begin{array}{ccc}f(1)=-4\\f(n+1)=f(n)+3\end{array}\right\\\\\text{Put n = 1 to the recursive formula:}\\\\f(1+1)=f(2)=f(1)+3\to f(2)=-4+3=-1`

Answer 2

The next term of the sequence is -1.

Explanation:

Given recursive formula,

f(n+1) = f(n) + 3,

For the second term,

Put n = 1,

`f(1+1) = f(1) + 3`,

`\implies f(2) = f(1) + 3`

Since, f(1) = - 4, ( given )

`\implies f(2) = -4 + 3 = -1`

Hence, the next term in the sequence would be -1,

Second option is correct.