Question

Use inductive reasoning to find the next two terms in the sequence.

3. 1/8, 2/7, 1/2, 4/5, ___, ___

4. -5, 3, -2, 1, -1, 0, ___, ___

7. 1, 5, 14, 30, 55, ___, ___

Answer 1

Induction means to guess what you think the pattern is. Do you see any patterns yet?

Answer 2

Here's a hint: rewrite that 1/2 in the first one as 3/6

Answer 3

#4 is a Fibonacci..

Answer 4

For #7, look at the differences between terms and see if they look familiar.

Answer 5

I got number 4 :D Thanks!!!

Answer 6

7. is increasing by square numbers... 4, 9, 16, 25, etc

Answer 7

I was hoping she'd notice that herself, campbell_st. :-/

Answer 8

Do you need another hint for the first one, @Adriana07 ?

Answer 9

is that why you said # was Fibonacci

Answer 10

I said #4 is Fibonacci. #7 I said to look at differences between terms.

Answer 11

well thats good... I'm using the same processes as you..

Answer 12

Woops sorry I got to into an essay I'm writing I forgot to check this ^-^
I understand 7 :D what exactly is a fibonacci?

Answer 13

Here's what's considered 'The Fibonacci sequence" (though Leonardo da Pisa gets too much credit for it)

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

Answer 14

Your #4 has the same style.

Answer 15

See what's going on there?

Answer 16

so it increases like 1,2,3,4,5,6....?

Answer 17

Not quite. See what you have to add to make the next number as you go along.

Answer 18

Could also start at zero: 0, 1, 1, 2, 3, 5, 8, . . .

Answer 19

I'm sorry I am so confused with this!

Answer 20

Look at the differences between the terms:
From 0 to 1 it's +1, from 1 to 1 it's +0, from 1 to 2 it's +1, from 2 to 3 it's +1, from 3 to 5 it's +2, etc.

So the pattern of additions to get to the next number is +1, +0, +1, +1, +2, +3, etc.

Answer 21

Each new number is the sum of the two that came before.

Answer 22

Now look at your #4.