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## In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic

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### In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic

by VJesus12 » Fri Feb 11, 2022 4:44 am

00:00

A

B

C

D

E

## Global Stats

In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic sequence $$a, b, c, d, e,$$ each term after the first is the sum of the preceding term and the constant $$k.$$ Which of the following is NOT an arithmetic sequence?

A. $$a, b - 1, c - 2, d - 3, e - 4$$

B. $$a - 1, b - 1, c - 1, d- 1, e - 1$$

C. $$a- 1, b - 2, c - 3, d- 4, e - 5$$

D. $$a, 2b, 3c, 4d, 5e$$

E. $$3a, 3b, 3c, 3d, 3e$$

Source: Princeton Review

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### Re: In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithm

by swerve » Fri Feb 11, 2022 1:36 pm
VJesus12 wrote:
Fri Feb 11, 2022 4:44 am
In an arithmetic sequence, each term after the first is the sum of the term before it plus a constant. In the arithmetic sequence $$a, b, c, d, e,$$ each term after the first is the sum of the preceding term and the constant $$k.$$ Which of the following is NOT an arithmetic sequence?

A. $$a, b - 1, c - 2, d - 3, e - 4$$

B. $$a - 1, b - 1, c - 1, d- 1, e - 1$$

C. $$a- 1, b - 2, c - 3, d- 4, e - 5$$

D. $$a, 2b, 3c, 4d, 5e$$

E. $$3a, 3b, 3c, 3d, 3e$$

Source: Princeton Review
We have arithmetic sequence:
$$a$$
$$b = a+k$$
$$c = a+2k$$
$$d = a+3k$$
$$e = a+4k$$

Checking options.
A.
$$b-1 = a+k-1$$
$$c-2 = a+2k-2$$
$$d-3 = a+3k-3$$
$$e-4 - a+4k-4$$

So the constant here is $$k-1.$$ Yes, it is an arithmetic sequence. And so on.

Therefore, D

It will be faster if we just check on numbers. $$a = 1, b = 2, c = 3, d = 4, e = 5.$$

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