Question

Which equation should be used to calculate S9 for the arithmetic sequence an=3n-1

o S9=9/2(2+26)
o S9= 9/2(4+17)
o S9=9/4(2+26)
o S9=9/4(4+26)

Answer 1

1. D

2. A

3. C

4. D

5. A

Step-by-step explanation:

Answer 2

Option A is correct.

The equation =
`S_9 =(9)/(2) (2+26)`.

Step-by-step explanation:

Sum of the terms of an arithmetic series is given by

`S_n = (n(a_1+a_n))/(2)`, ......[1]

where n is the number of terms,
`a_1` is the first term and
`a_n`is the last term.

Given the formula for nth term in the arithmetic sequence is,
`a_n = 3n-1`

for n =1

`a_1 = 3 \cdot 1 -1 = 3-1 =2`

for n =9

`a_9= 3 \cdot 9 -1 = 27-1 =26`

Then, put these values in equation [1] for n =9;

`S_9 = (9 \cdot (a_1+a_9))/(2) = (9(2+26))/(2)` or

`S_9 =(9)/(2) (2+26)`

Therefore, the equation is;
`S_9 =(9)/(2) (2+26)`