Question

I just need someone to check this answer for me.

Answer 1

\[\large \sum_{n=5}^{12}(4 - 3n)\]

Answer 2

You need to find the sum of the arithmetic series (shown above).

Answer 3

what is n_5=[4-3(5)] and n_12=[4-3(12)]

Answer 4

My work:

n = 8

a_1 = -1
because the common difference = -3
-3(n-1) + n_1 = f(n)
-3n + 3 = n_1 = f(n)
-3(5) + 3 + n_1 = -11
-15 + 3 + n_1 = -11
-12 + n_1 = -11
n_1 = 1

a_n = -32
because 4 - 3(12) = -32


\[\frac{ 8 }{ 2 }(-1 - 32) = 4(-33) = - 132 \]

Answer: -132

Answer 5

sorry i made a mistake
4(1 - 32) = 4(-31) = -124

Answer 6

answer: -124

Answer 7

i got something else.

Answer 8

Ill take you step by step - n_5=[4-3(5)] ?

Answer 9

-11

Answer 10

n_12=[4-3(12)] ?

Answer 11

-32

Answer 12

\[s_n=\frac{ n }{ 2 }[a_1+a_n]\] a_1=-11 and a_n=-32 and n=8

Answer 13

i thought that a_1 = 1 because when u use the explicit formula
-3(n - 1) + n_1 = f(n)
-3n + 3 + n_1 = f(n)
-3(5) + 3 + n_1 = -11
-12 + n_1 = -11
n_1 = 1

Answer 14

your first term starts at 5

Answer 15

therefore you are plugging in 5

Answer 16

i thought n = the term number so n = 5 is the fifth term

Answer 17

a_1 just represents the first term which in your case is a_5

Answer 18

The lower index tells you where your sequence/ series will start. As you can see yours will start at 5. Therefore you are plugging in 5 for your a_1. Keep in mind that a_1 represent your first number in the sequence.

Answer 19

so a_1 = 5 ?

Answer 20

a_5=-11

Answer 21

-11 is your first term

Answer 22

Think of it this way, if you started at 1 that would give you 12 terms because 1,2,3,4,5,6,7,8,9,10,11,12. But we are starting at 5 therefore only 8 terms.

Answer 23

okay so when i have the lower index, i just need to plug it into the equation and then get my a_1 value

Answer 24

Correct.

Answer 25

ok thanks for the help :)

Answer 26

Then plug in your upper index to get your last term.

Answer 27

Glad that helped c:

Answer 28

which is the a_n right?

Answer 29

In the end you should get -129 as the sum of this sequence. Yes, a_n represents the last term in the sequence.

Answer 30

so i would have 4(-11 - 32) ?