Question

A sequence has its first term equal to 8 and each term of the sequence is obtained by adding 6 to the previous term. If f(n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence?

f(1) = 6 and f(n) = f(n - 1) + 8; n > 1

f(1) = 8 and f(n) = f(n - 1) + 6; n > 1

f(1) = 8 and f(n) = f(n - 1) + 6n; n > 1

f(1) = 6 and f(n) = f(n - 1) + 8n; n > 1

Answer 1

A sequence has its first term equal to 8

can you rule out any of the 4 choices ?

Answer 2

im thinking the third one

Answer 3

Hopefully it is clear that
A sequence has its first term equal to 8
means f(1)=8

so the first and last choices are definitely out.

Answer 4

each term of the sequence is obtained by adding 6 to the previous term.

we can list a few terms, to see what the sequence looks like. It starts at 8
8
and then add 6 to get the next number: 8+6= 14
then add 6 to that to get the third number: 14+6= 20

so
8,14,20,26, and so on.

Answer 5

Let's try your choice:
f(1) = 8 and f(n) = f(n - 1) + 6n; n > 1

when n=1, we get f(1)=8 (which is good)
when n=2 we do
f(2)= f(2-1) + 6*2 (replace n with 2 everywhere you see n)
simplify to get: f(2) = f(1) + 12
f(1) is 8 (from the first step. so: f(2)= 8+12= 20

according to the rule, f(2)= 20
but the sequence goes 8,14,20,26...

f(2) is 14. This rule is not the one we want.

Answer 6

oh ok so it would be second one

Answer 7

you can even check the 2nd choice:
f(1) = 8 and f(n) = f(n - 1) + 6; n > 1

f(2)= f(2-1) + 6
f(2) = f(1) + 6
f(2) = 8+6 = 14
which works.

This stuff is not too hard if you practice it.

Answer 8

yea im not to great with math i try to study a lot but im not to good

Answer 9

but is it ok if u could help me with one more question if possible?