Question

I need to find the answer to B

Answer 1

a) The next two terms are: 13, 16

b) nth term of the sequence is
`\mathbf{a_n=3n-5}`

Explanation:

a) Find the next two terms of sequence: -2,1,4,7 and 10

The common difference d: a₂-a₁ = 1-(-2)= 3

a₃-a₂= 4-1 = 3

a₄-a₃=7-4=3

So, common difference is : 3

Next two terms are: 10+3 = 13

13+3= 16

The next two terms are: 13, 16

b) Find nth term of the sequence

The nth term can be found using formula:

`a_n=a_1+(n-1)d`

where a₁=First term and d=Common Difference

In the sequence given we have a₁=-2 and d=3

So, the nth term will be:

`a_n=a_1+(n-1)d\\a_n=-2+(n-1)3\\a_n=-2+3n-3\\a_n=3n-5`

So, nth term of the sequence is
`\mathbf{a_n=3n-5}`