Question

Which arithmetic sequence has a common difference of -21? ( only one is correct )

a) {873, 894, 915, 936, …}

b) {32, 20, 8, -4, …}

c) {1,245; 1,224; 1,203; 1,182; …}

d) {1,563; 1,587; 1,611; 1,635; …}

Answer 1

Answer: c) {1,245; 1,224; 1,203; 1,182; …}

Step-by-step explanation:

Concept:

For this question, we just go by eliminating each answer until we get the correct one

Given information

Common difference = -21 (decreasing sequence)

Answer Choice: a) {873, 894, 915, 936, …}

894 - 873 = 21

915 - 895 = 21

936 - 915 = 21

Since the common difference is 21, not -21

$\large\boxed{FALSE}$

Answer Choice: b) {32, 20, 8, -4, …}

20 - 32 = -12

8 - 20 = -12

-4 - 8 = -12

Since the common difference is -8, not -21

$\large\boxed{FALSE}$

Answer Choice: c) {1,245; 1,224; 1,203; 1,182; …}

1224 - 1245 = -21

1203 - 1224 = -21

1182 - 1203 = -21

Since the common difference is -21

$\Huge\boxed{TRUE}$

Answer Choice: d) {1,563; 1,587; 1,611; 1,635; …}

1587 - 1563 = 24

1611 - 1587 = 24

1635 - 1611 = 24

Since the common difference is 24, not -21

$\large\boxed{FALSE}$

Hope this helps!! :)

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