Question

Use sigma notation to represent the sum of the first six terms of the following sequence: −10, −13, −16, …

Answer 1

Answer:

"the summation from n equals one to 6 of quantity negative 7 minus 3 times n"

Step-by-step explanation:

General term of an arithmetic sequence:

$a_n=a_1+(n-1)r$

Where

$a_1$ is the first term

n is the number of terms

r is the common difference

The value of r can be found by subtracting two consecutive values

$r=a_2-a_1=-13+10=-3$

Then

$a_n=-10+(n-1)(-3)=-7-3n$

If we want to sum the first six terms of the sequence, we must find

$\sum_{n=1}^{n=6}(-7-3n)$

The correct option is

"the summation from n equals one to 6 of quantity negative 7 minus 3 times n"