Question

Hey guys I’m really struggling with these questions I know there’s alot all at once but if you can help me with either I would be really grateful. Thanks very much!

Answer 1

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Answer:

  17. an = 4 +7(n -1)

  18. an = 35 -4(n -1)

  19. an = 21 +6(n -1)

  20. an = 2 +5(n -1)

Step-by-step explanation:

There are two numbers that tell you everything you need to know about an arithmetic sequence:

• the first term (a1)
• the common difference (d)

Using these two numbers, you can write the expression for the n-th term of the sequence as ...

  an = a1 + d(n -1)

This is true for any arithmetic sequence.

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The first term is the first one listed, so is not hard to find.

The common difference is the difference between the second term and the first term: d = a2 -a1. Usually, you can do this subtraction in your head, so "by inspection" you can find the first term and common difference. For example, in problem 17, it is d = 11 -4 = 7.

_____

17. an = 4 +7(n -1)

18. an = 35 -4(n -1)

19. an = 21 +6(n -1)

20. an = 2 +5(n -1)