Answer:
a) The next two terms are: 13, 16
b) nth term of the sequence is [tex]\mathbf{a_n=3n-5}[/tex]
Step-by-step 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:
[tex]a_n=a_1+(n-1)d[/tex]
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:
[tex]a_n=a_1+(n-1)d\\a_n=-2+(n-1)3\\a_n=-2+3n-3\\a_n=3n-5[/tex]
So, nth term of the sequence is [tex]\mathbf{a_n=3n-5}[/tex]
