Question

What is the general term for sequence -6;3;15;30?​

Answer 1

`(3)/(2) n {}^(2) + (9)/(2) n - 12`

Explanation:

This sequence is a quadratic sequence meaning that we should find the difference and the constant second difference.

The difference between the 4 terms is in the sequence:

9;12;15

The constant second difference is 3.

Use your method of finding the general term:

2a=3 3a+b=9 a+b+c=-6

a=3/2 3(3/2)+b=9 3/2+9/2+c=-6

b=9/2 c=-12

Standard form for quadratic sequence:

`{an}^(2) + bn + c`

Therefore your general term is the one stated above in the answer.

Hope that helps!