Write the first six terms of the arithmetic sequence with the given properties. $a = 3,3$ rd term is $- 5$
A) $\quad 7,3 , - 5 , - 5 , - 9 , - 13$
B) $\quad 3,7 , - 5,15,19,23$
C) $\quad 7,11 , - 5,19,23,27$
D) $\quad 3 , - 1 , - 5 , - 9 , - 13 , - 17$
E) none of the above

Question

Quizplus · Accepted Answer

We know that the common difference between each term in an arithmetic sequence is the same. Let's call the common difference "d".

We're given that the first term (a[1]) is 3, so we know:

a[1] = 3

We're also given that the third term (a[3]) is -5, so we know:

a[3] = a[1] + 2d = -5

Solving for d:

a[1] + 2d = -5

3 + 2d = -5

2d = -8

d = -4

Now that we know d, we can find the rest of the terms.

a[1] = 3

a[2] = a[1] + d = 3 + (-4) = -1

a[3] = a[1] + 2d = 3 + 2(-4) = -5

a[4] = a[3] + d = -5 + (-4) = -9

a[5] = a[4] + d = -9 + (-4) = -13

a[6] = a[5] + d = -13 + (-4) = -17

So the first six terms of the arithmetic sequence are:

3, -1, -5, -9, -13, -17

which is answer choice D.

Write the First Six Terms of the Arithmetic Sequence with the Given