Question

i need the answer asap 20 points

In an arithmetic sequence, the first term, a_1,a
1 , is equal to 5,5, and the fifth term, a_{5},is equal to 41.41. Which number represents the common difference of the arithmetic sequence?

Answer 1

Answer:

  10

Step-by-step explanation:

The general term of an arithmetic sequence is given by ...

  an = a1 +d(n -1) . . . . where a1 is the first term and d is the common difference

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This formula can be used to find the value of d. The first term is given as 1, and the 5th term (a5) is given as 41. The value of n for the 5th term is 5.

  an = a1 +d(n -1)

  41 = 1 +d(5 -1) . . . . . substitute known values

  40 = 4d . . . . . . . subtract 1, simplify

  10 = d . . . . . . divide by 4

The common difference of this sequence is 10.