Question

Use inductive reasoning to determine the next three numbers in the list of numbers below. 50,25,9-25,-50,__,__,__.

Answer 1

Step-by-step explanation:

See.. there are two solution for this question…

First one:—

(1×1)=1

(2×2)=4

(3×3)=9

(4×4)=16

(5×5)=25

(6×6)=36

(7×7)=49

(8×8)=64

(9×9)=81

(10×10)=100…. So as you saw that the pattern above is the square of consecutive numbers from 1 to 7… nd the rest are the square of 8..9 nd 10…

Bow second method…

The series above is…

1…4…9…16…25…36…49

Here…

4-1=3

9-4=5

16-9=7

25-16=9

36-25=11

49-36=13…

So u can see that the difference between each term is a prime number ….and they form a series itself…

Series of odd no…..u can call it in Airthmetic progression too…

3..5..7..9..11..13.. nd the next odd no. Are 15..17 nd 19….

So the next 3 no. In the pattern are…

49+15=64

64+17=81

81+19=100

Firstly, we have to do that multiply to same number. It means multiplication.

Let’s see the interesting thing.

(1×1) , (2×2) , (3×3) ……… . ……… (10×10). Like that.

Here the sequence is 1, 4, 9, 16, 25, 36, 49, ….?

So now,

We have to apply those interesting method.

( 1 × 1 ) = 1

( 2 × 2 ) = 4

( 3 × 3 ) = 9

( 4 × 4 ) = 16

( 5 × 5 ) = 25

( 6 × 6 ) = 36

( 7 × 7 ) = 49

( 8 × 8 ) = 64

( 9 × 9 ) = 81

( 10 × 10 ) = 100

The next 3 terms is 64, 81, 100

This pattern will be end like 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

I think it's definitely clear to you all.

Thanks everyone.