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6 votes
Position
1 2 3 4 5 n
Value of term
2 12 17 22 27

Position 1 2 3 4 5 n Value of term 2 12 17 22 27-example-1
User Sharee
by
7.8k points

1 Answer

10 votes

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:


  • a_n=5n+2

Explanation:

Given the sequence

7, 12, 17, 22, 27

Here, the first element of the sequence is:


a_1=7

An arithmetic sequence has a constant difference 'd' and is defined by


a_n=a_1+\left(n-1\right)d

computing the differences of all the adjacent terms


12-7=5,\:\quad \:17-12=5,\:\quad \:22-17=5,\:\quad \:27-22=5

The difference between all the adjacent terms is the same and equal to


d=5

so substituting d = 5 and
a_1=7 in the nth term to determine the expression


a_n=a_1+\left(n-1\right)d


a_n=5\left(n-1\right)+7


a_n=5n+2

Therefore, the expression for the nth term of the givens sequence is:


  • a_n=5n+2
User David Blaney
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6.8k points