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olasank [31]
3 years ago
5

An arithmetic series consists of consecutive integers that are multiples are of 4. What is the sum of the first nine terms of th

is sequence if the first term is 0
Mathematics
2 answers:
Maslowich3 years ago
6 0

Answer:

144

Step-by-step explanation:

The series is described by the problem statement as ...

... 0 +4 +8 +12 +... +32

= 4*(0 +1 +2 +... +8) . . . . . the first 9 multiples of 4, starting with 0

Now we know the sum of integers 1..n is given by n(n+1)/2. So for n=8, this is ...

... 8·9/2 = 36

Multiplying this by 4, we find the series sum to be ...

= 4·(sum of integers 0 .. 8) = 4·36 = 144

_____

<em>Comment on the answer choices</em>

It appears your answer choices may not include the value 144. That is unfortunate. You may want to <em>ask your teacher to show you how to work this problem</em> and reconcile the answer choices with the problem statement.

The 9-term series <u><em>starting with 4</em></u> will have sum ...

... 4·(1 +2 +3 +... +9) = 4·(9·10)/2 = 4·45 = <em>180</em>

Ahat [919]3 years ago
3 0

Answer:

144

Step-by-step explanation:

Remark

Well you could do this the brute force way. 32 is the nineth term in the series.  Sum = 0 + 4 + 8 + 12 + ... 32 = 144. That will get you an answer.

This works unless you are asked for the 44434th term. Then you better use a formula. Even the hundredth term would be trouble.

Step One

Find d

d is given as 4

Step 2

find n. There are 9 terms. The 9 is given.

Step 3

Find the ninth term.

<em><u>Givens</u></em>

a1 = 0

n = 9

d = 4

<em><u>Formula for the 9th term: </u></em>a9 = a1 + (n - 1)*d

Substitute and Solve

a9 = 0 + (9 - 1)*4

a9 = 8*4 = 32

Step 4

Find the sum of the first 9 terms

Sum = (a1 + a9)*n/2

Sum = (0 + 32)*9/2

Sum = 32 * 9/2

Sum = 32 * 4.5

Sum = 144



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