Question

Which of the following is an arithmetic sequence with common difference –5?

8, 3, –2, –7, . . .

B)

0, 5, 10, 15, . . .

C)

5, 25, 125, 625, . . .

D)

5, –25, 125, –625, . . .

Answer 1

8, 3, –2, –7, . . .

Explanation:

Answer 2

Option A i.e. 8, 3, -2, -7, ... is correct.

Explanation:

Let us check the sequence given in option A

`8, 3, -2, -7, . . .`

An arithmetic sequence has a constant difference '
`d`' and is defined by

`a_n=a_1+\left(n-1\right)d`

determine the differences of all the adjacent terms of Arithmetic sequence

`3-8=-5,\:\quad \:-2-3=-5,\:\quad \:-7-\left(-2\right)=-5`

The difference between all the adjacent terms is the same and equal to

`d=-5`

Therefore, we conclude that the arithmetic sequence 8, 3, -2, -7, ... has a common difference -5.

Hence, option A i.e. 8, 3, -2, -7, ... is correct.