Question

"Which of the following sequences of numbers are arithmetic sequences? Check all that apply.

"

Answer 1

Option B, C, D

Explanation:

We have to find the arithmetic sequence from the sequences given in the question.

To solve this question we will use the property of an arithmetic sequence that every successive term of an arithmetic sequence has a common difference.

(A) 1, -2, 3, -4, 5 .....

`d_(2)-d_(1)` = -2 -1 = -3

`d_(3)-d_(2)` = 3 - (-2) = 3 + 2 = 5

Sequence is not an arithmetic sequence

(B) 154, 171, 188, 205, 222 .....

`a_(2)-a_(1)` = 171- 154 = 17

`a_(3)-a_(2)` = 188 - 171 = 17

The sequence is an arithmetic sequence having common difference = 17

(C) 12,345, 12,346, 12,347......

`a_(2)-a_(1)` = 12,346 - 12,345 = 1

`a_(3)-a_(2)` = 12,347 - 12,346 = 1

Therefore, the sequence is an arithmetic sequence

(D) -3, -10, -17, --24, -31

`a_(2)-a_(1)` = -10 + 3 = ( -7 )

`a_(3)-a_(2)` = -17 + 10 = ( -7 )

This sequence is an arithmetic sequence

(E) 1, 8, 16, 24, 32 ....

`a_(2)-a_(1)` = 8 - 1 = 7

`a_(3)-a_(2)` = 16 - 8 = 8

Difference in terms is not common. Therefore, sequence is not an arithmetic sequence.

Option B,C,D are arithmetic sequences.

Answer 2

B) 154, 171, 188, 205, 222
A constant value (17) is added to get the next number