Question

What is the general term equation, an, for the arithmetic sequence 5, 1, −3, −7, . . . , and what is the 21st term of this sequence?

Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.

an = 17 − 4n, a21 = −67
an = 17 + 4n, a21 = 101
an = 13 − 4n, a21 = −71
an = 9 − 4n, a21 = −75

Answer 1

The common difference, d, can be determined by subtracting the two consecutive values:

1 - 5 = -4
-3 - 1 = -4
-7 - -3 = -4

Then, using the equation:

an = a1+ d(n-1)
a_21 = 5 + (-4)(21 - 1)
a_21 = -75

The answer is letter D. I hope I was able to help you. Have a good day!