Question

Write an explicit formula for the arithmetic sequence: -2,7,16,25,...

Answer 1

Answer:

a_n = 9n - 11

Step-by-step explanation:

Explicit rule for an arithmetic sequence is a_n = a_1 + (n-1) d

a_1 is the first term of the sequence

d is the common difference. To find d you pick a number in the sequence and subtract it by the previous number. For example, 7 - (-2) = 9

16 - 7 = 9 so, d = 9

a_1 = -2 since it is the first term. Now substitute these numbers into the formula.
a_n = -2 + (n-1)(9)

And then we simplify.
9 • n = 9n

9 • -1 = -9
Then we’ll have a_n = -2 + 9n -9 and well simplify even further.
-2 -9 = -11

So we get

a_n= 9n -11

hope that helped! God bless you!!