The first four terms of a quadratic sequence are shown below. 6, 9, 14, 21, . . . What is the difference between the 5th term and the 6th term of the quadrati

Question

Difference between terms in a sequence

Answer 1

The long way to solve this problem is to determine the underlying quadratic function, calculate the fifth and sixth terms, then take their difference.

 

On an exam with this kind of problem, the students who detect the pattern will finish the test with time to spare.  The students who take the long way may not have enough time to complete the exam.

 

The pattern of the terms is 6, 9, 14, 21, where 3 is added to the first term to get the second, 5 to the second to get the third, and 7 to the third to get the fourth.

 

The difference between the fourth and fifth terms will be the next odd number, 9, and the difference you seek, that between the fifth and sixth terms is 11.

 

 

 

Answer 2

by looking at the first four terms.... you can see  that they increase +3, +5, +7...

it would stand to reason that the fifth term is +9 from 21 and the 7th term is +11 from the sixth term