Question

What would the second and third terms of an arithmetic sequence be if the first term is 6 and the fourth is 33?

Answer 1

The second term = 15, and the third term = 24

Explanation:

An arithmetic sequence can be written on the form
`s_n=an+b`
We know that `s_1=6` and `s_4=33`
Therefore: `s_4-s_1`=(4a+b)-(a+b)`=33-6=27`
`3a=27`
`a=9`
As `6=9+b`,
`b=-3`
Therefore `s_n=9n-3`
We, therefore, get:
`s_1=1*9-3=6`
`s_2=2*9-3=15`
`s_3=3*9-3=24`
`s_4=4*9-3=33`