Question

Which sequences are arithmetic? Check all that apply.

–5, 5, –5, 5, –5, …
96, 48, 24, 12, 6
18, 5.5, –7, –19.5, –32, …
–1, –3, –9, –27, –81, …
16, 32, 48, 64, 80

Answer 1

c, and e

Explanation:

Answer 2

3) 18, 5.5, –7, –19.5, –32, … sequence is in Arithmetic Progression.

5) 16, 32, 48, 64, 80 sequence is in Arithmetic Progression.

Explanation:

If, a, b, c ,k, e ... is a given sequence.

Then the above sequence is in AP if b - a = c - b = k - c = ...

or, each term has same COMMON DIFFERENCE (d).

Here, take each sequence and check for the value of d.

1) –5, 5, –5, 5, –5, …

Here, 5 - (-5) = 10, -5 - 5 = -10

and 10 ≠ -10. So the sequence is NOT in Arithmetic Progression.

2)96, 48, 24, 12, 6

Here, 48 - 96 = -48, 24 - 48 = -24

and -48 ≠ -24. So the sequence is NOT in Arithmetic Progression.

3)18, 5.5, –7, –19.5, –32, …

Here, 5.5 - 18 = -12.5 , -7 - 5.5 = -12.5 ..

and -12.5 is the common difference.

So the sequence is in Arithmetic Progression.

4)–1, –3, –9, –27, –81, …

Here, -3-(-1) = - 2 -9 - (-3) = -6

and -2 ≠ -6. So the sequence is NOT in Arithmetic Progression.

5)16, 32, 48, 64, 80

Here, 32 - 16 = 16 , 48 - 32= 16 ..

and 16 is the common difference.

So the sequence is in Arithmetic Progression.