Question

Jeremy is writing down a sequence of integers. He writes 1 as his first number. Then, he

squares it and adds 3, writing down 4 next. He squares 4 and adds 3, writing down 19 as his third
number. If Jeremy continues his square-and-add pattern, what will the units digit of the 20th
number in his list be?

Answer 1

4 is the unit's digit of the 20th number.

Explanation:

Let us try to find out a pattern for the unit's digit of the terms.

1st term is 1, so unit's digit of 1st term is 1.

2nd term
`1^(2) + 3 = 4` so unit's digit is 4.

3rd term
`4^(2) + 3 = 19` so unit's digit is 9.

4th term
`19^(2) + 3 = 364` so unit's digit is 4.

5th term's unit digit: Square of unit's digit of 4th term + 3

`4^(2) + 3 = 19` i.e. 9.

:

We can see that the pattern is

3rd, 5th, 7th ...... terms have 9 as the unit's digit.

2nd, 4th, 6th.... terms have 4 as the unit's digit.

So, 20th term will have 4 as the unit's digit.