Question

The first five terms of a sequence are 7 10 13 16. 19

Witch of the following functions define this sequence for all integers n>= 1?

Answer 1

OPTION B: f(n) = 4 +3n

Explanation:

Substitute n =1 in each of the options. We compare the given sequence and the result obtained.

OPTION A: f(n) = 4(3)
`$ ^(n - 1) $`

Substituting n =1, we get: f(1) =
`$ 4(3)^(0) $` = 4.

But, in the given sequence the first term is 7. So, this is not the recursive form.

OPTION B: f(n) = 4 + 3n

Substituting n = 1 2, 3, 4, 5

f(1) = 4 + 3(1) = 7

f(2) = 4 + 3(2) = 10

f(3) = 4 + 3(3) = 13

f(4) = 4 + 3(4) = 16

f(5) = 4 + 3(5) = 19

This is exactly the sequence given.

So, we say OPTION B is the answer.

OPTION C: f(n) = 3n + 7

Substituting n = 1.

f(1) = 3(1) + 7 = 10

It is discarded.

OPTION D: f(n) =
`$ 7(3)^(n - 1) $`

Substituting n = 1.

f(1) =
`$ 7(3)^(0) $` = 7

Substituting n = 2

f(2) =
`$ 7(3)^(1) = 7(3) = 21 $`

This option can be discarded as well.