# Sequence II

This question given in the Primary group of the 1^{st} International Vedic Mathematics Olympiad (IVMO 2021):

“What are the next two numbers in this sequence?

97 79 64 52 __ ___

A 42 36 B 44 38 C 44 37 D 43 38 E 43 37

We can see that unlike in our previous post about sequences, (https://www.math-inic.com/blog/sequences-i/) the difference between terms is not equal but decreasing by a fixed amount.

97 – 79 = 18

79 – 64 = 15; 18 – 15 = 3

64 – 52 = 12; 15 – 12 = 3

This is called a quadratic sequence. We can find a formula for getting the nth term of the sequence but since we are only asked for the next two terms, we do not have to solve for it.

Since the common difference between the “1^{st} differences” is 3, we know that the next two terms will be (12 – 3 = 9) and (9 – 3 = 6) less than the fourth and fifth terms respectively.

So, they will be (52 – 9 = 43) and (43 – 6 = 37) respectively.

Letter E is the correct answer.