Question

COMPLETION 59% Here are the first five terms of a number sequence. -4 -1 2 5 8 Find, in terms of n, an expression for the nth term of this number sequence.​

Answer 1

`a_n=3n-7`

Explanation:

We use arithmetic sequences to derive a formula for the nth term

• the general formula for an arithmetic sequence is:
  `a_(n) = a_(1) + (n-1)d`
• Where
  `a_(n)` is the nth term,
  `a_(1)` is the first term and
  `d` is the common difference

We substitute only for
`a_(1)` and
`d`

`a_1 = -4\\d = (\text{2nd term - 1st term})=(-1-(-4))=3`

Then we substitute

• 
  `a_n=-4+3(n-1)=-4+3n-3=3n-7`

We can test it:

the 5th term is 8, so:

`a_n=3n-7\\a_5=3(5)-7\\a_5=15-7=8`