Question

Describe an infinte geometric series with a beginning vaule of 2 that converges to 10. What are the first 4 terms of the series?

I know r=4/5

Now what do I do

Answer 1

just plug and chug.

4/(1-r) = 10
2/5 = 1-r
r = 3/5

So, now you know the G.P.

Answer 2

[AI-generated answer — Explain Bot]

To find the first 4 terms of the infinite geometric series with a beginning value of 2 and a common ratio of 4/5 that converges to 10, you can use the formula for the general term of a geometric series:

𝑎𝑛 = 𝑎₁ * 𝑟^(𝑛−1)

where 𝑎𝑛 is the 𝑛-th term of the series, 𝑎₁ is the first term, 𝑟 is the common ratio, and 𝑛 is the position of the term in the series.

In this case, 𝑎₁ = 2 (the first term) and 𝑟 = 4/5 (the common ratio).

To find the first term, substitute 𝑛 = 1 into the formula:

𝑎₁ = 2 * (4/5)^(1-1)

Simplifying this, we have:

𝑎₁ = 2 * (4/5)^0
= 2 * 1
= 2

Therefore, the first term (𝑎₁) of the series is 2.

To find the second term, substitute 𝑛 = 2 into the formula:

𝑎₂ = 2 * (4/5)^(2-1)
= 2 * 4/5
= 8/5
= 1.6

So, the second term (𝑎₂) of the series is 1.6.

Similarly, you can find the third term (𝑎₃) and the fourth term (𝑎₄) by substituting 𝑛 = 3 and 𝑛 = 4 into the formula.