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What is the sum of the first eight terms of the geometric series 2 + 6 + 18 + 54+ ...? 510 3,280 6,560 4,374

2 Answers

2 votes

Answer:

6,560

Explanation:

User LShapz
by
7.2k points
8 votes

Answer:

6,560

Explanation:

We are given the first four terms of the sequence:

2, 6, 18, 54, ...

We need to find another four terms to find the sum.

I don't know how to explain how I got the pattern but you have to multiply by 3:

2 * 3 = 6

6 * 3 = 18

18 * 3 = 54

To find the next term, we will multiply 54 by 3:

54 * 3 = 162

2, 6, 18, 54, 162, ...

We now have 5 terms.

Next, multiply 162 by 3:

162 * 3 = 486

2, 6, 18, 54, 162, 486, ...

We now have 6 terms.

Next, multiply 486 by 3:

486 * 3 = 1458

2, 6, 18, 54, 162, 486, 1458, ...

We now have 7 terms.

Lastly, multiply 1458 by 3:

1458 * 3 = 4374

2, 6, 18, 54, 162, 486, 1458, 4374, ...

We now have the first 8 terms.

Now, we add all these numbers together:

2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 = 6560

The sum of the first eight terms of the geometric sequence is 6,560

User Hyomin
by
7.6k points