Note: It seems the first term of your sequence is 7 instead of 2. So, I am assuming you meant the sequence such as;
7, 12, 17, 22, 27
Answer:
The expression for the nth term of the givens sequence is:
Step-by-step explanation:
Given the sequence
7, 12, 17, 22, 27
Here, the first element of the sequence is:
[tex]a_1=7[/tex]
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
[tex]12-7=5,\:\quad \:17-12=5,\:\quad \:22-17=5,\:\quad \:27-22=5[/tex]
The difference between all the adjacent terms is the same and equal to
[tex]d=5[/tex]
so substituting d = 5 and [tex]a_1=7[/tex] in the nth term to determine the expression
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=5\left(n-1\right)+7[/tex]
[tex]a_n=5n+2[/tex]
Therefore, the expression for the nth term of the givens sequence is:
