Question

Use inductive reasoning to find the next term in the sequence 1, 2, 4, 7, 11, 16…

What is the next term?
(Points : 1)
18
19
22
26

Answer 1

I will try to give you a little hint.

(1st difference) \(\large\color{black}{ \displaystyle \color{red}{{\rm d}_1=}a_2-a_1=2-1=\color{red}{1} \\[0.3em] }\)
(2nd difference) \(\large\color{black}{ \displaystyle \color{red}{{\rm d}_2=}a_3-a_2=4-2=\color{red}{2} \\[0.3em] }\)
(3rd difference) \(\large\color{black}{ \displaystyle\color{red}{{\rm d}_3=}a_4-a_3=7-4=\color{red}{3} \\[0.3em] }\)
(4th difference) \(\large\color{black}{ \displaystyle\color{red}{{\rm d}_4=}a_5-a_4=11-7=\color{red}{4} \\[0.3em] }\)
(5th difference) \(\large\color{black}{ \displaystyle\color{red}{{\rm d}_5=}a_6-a_5=16-11=\color{red}{5} \\[0.3em] }\)

Answer 2

see that the difference is growing by 1, and in fact, and nth difference is "n"


(where n is integer of course, since n denotes not only the difference, but the order of the term)

Answer 3

i dont understand?

Answer 4

When you just say "I don't understand" that doesn't tell me what your concern is.

Anything specific?

Answer 5

like..i dont understand how i would find the next term?