Question

The tenth through thirteenth terms of an arithmetic sequence are given by a10=47, a11=53. a12=59, and a13=65. Which formula can be used to find a n?

A. an=6n-13
b. an=6n+37
c. an=6n+41
d. an=6n-47
e, an=6n-7

Answer 1

Answer: e, an=6n-7.

Step-by-step explanation: Any pair of consecutive terms can be used to determine the arithmetic sequence's common difference (d), which can then be used in conjunction with the given term to determine the nth term using the following formula:

an = a1 + (n - 1) d.

Let's use the pair a11=53 and a10=47 to find d:

d = a11 - a10 = 53 - 47 = 6

Now we can use the formula to find any term of the sequence. Let's use the given value of a13=65 to find a13:

a13 = a1 + (13 - 1)d

65 = a1 + 12(6)

65 = a1 + 72

a1 = -7

Therefore, the formula that can be used to find the nth term of the arithmetic sequence is:

an = -7 + (n - 1)6

Simplifying this expression, we get:

an = 6n - 7.