Question

A sequence is defined recursively by the formula f(n + 1) = –2f(n). The first term of the sequence is –1.5. What is the next term in the sequence? –3.5 –3 0.5 3

Answer 1

Answer: 3.

Explanation:

Given : A sequence is defined recursively by the formula
`f(n + 1) = -2f(n)`

The first term of the sequence is -1.5.

i.e.
`f(1)=-1.5`

To find the next term , we put n=1 in the given expression, we get

`f(1 + 1) = -2f(1)\\\\\Rightarrrow\ f(2)=-2(-1.5)=3`

Hence, the next term in the sequence is 3.

Answer 2

3

Explanation:

Put the given numbers in the formula and do the arithmetic.

f(2) = -2·f(1) = -2·(-1.5) = 3

The next term of the sequence is 3.