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

Answer:

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

Step-by-step 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.