To find an infinite geometric series that converges to 10 with a beginning value of 2, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r)
Where:
S = sum of the infinite series
a = the beginning value of the series (2 in this case)
r = the common ratio
Since the series converges to 10, we can set S = 10:
10 = 2 / (1 - r)
Now, solve for r:
10 = 2 / (1 - r)
10(1 - r) = 2
10 - 10r = 2
-10r = -8
r = 0.8
Now that we have the common ratio, we can find the first 4 terms of the series:
Term 1 = 2
Term 2 = 2 * 0.8 = 1.6
Term 3 = 1.6 * 0.8 = 1.28
Term 4 = 1.28 * 0.8 = 1.024
Therefore, the first 4 terms of the infinite geometric series with a beginning value of 2 that converges to 10 are: 2, 1.6, 1.28, 1.024.
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Describe an infinite geometric series with a beginning value of 2 that converges to 10. What are the first 4 terms of the series?
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