Question

Use inductive reasoning to find the next term in the sequence 2, 3, 5, 8, 12 …

What is the next term?

A.
13

B.
15

C.
17

D.
18

Answer 1

\(\large\color{black}{ \displaystyle 2+3=~? }\)

Answer 2

5

Answer 3

so we once saw, that the next term is the sum of the two terms before it.
(that is, the 3rd term 5, is the sum of the 1st term 2 and the 2nd term 3)

Answer 4

\(\large\color{black}{ \displaystyle 3+5=~? }\)

Answer 5

8

Answer 6

yes, and here we see again the same thing

some term = sum of the two terms right before it

Answer 7

are you sure you have written the sequence correctly? Are you sure the last number in sequence is 12 and not 13?

Answer 8

yes

Answer 9

oh, then it follows a different patten

\(\large\color{black}{ \displaystyle 2+\color{red}{1}=3}\)
\(\large\color{black}{ \displaystyle 3+\color{red}{2}=5}\)
\(\large\color{black}{ \displaystyle 5+\color{red}{3}=8}\)
\(\large\color{black}{ \displaystyle 8+\color{red}{4}=12}\)

Answer 10

see that your difference (that you are adding, that I colored in red) is growing by 1 each time?

Answer 11

yes

Answer 12

so what would you add to 12 to get to the next term?

Answer 13

5

Answer 14

yes, and so your next term after 12 is?

Answer 15

\(\large\color{black}{ \displaystyle 12+\color{red}{5}=~?}\)

Answer 16

17

Answer 17

yup

Answer 18

thx

Answer 19

yw