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Answered

How many terms are there in a geometric series if the first term is 3, the common ratio is 4, and the sum of the series is 1,023?

Verified Answer :

In Geometric Progression, we know S(n) = a.(rⁿ - 1 ) / r - 1
Here, a = 3, r = 4 a(n) = 1,023
1023 = 3 (4ⁿ - 1) / (4 - 1)
3(4ⁿ - 1) = 1023 * 3
4ⁿ - 1 = 3069 / 3
4ⁿ = 1023 + 1
4ⁿ = 1024
4⁵ = 1024

In short, Your Answer would be 5 Terms

Hope this helps!



Cricetus

There are five terms. A complete solution is provided below.

Given values are:

First term,

  • a₁ = 3

Common ratio,

  • r = 4

Sum,

  • Sn = 1023

As we know,

→ \(S_n = \frac{a_1 (1-r^n)}{1-r}\)

By substituting the given values, we get

→ \(1023 = \frac{3(1-4^n)}{1-4}\)

→ \(1023= \frac{3(1-4^n)}{3}\)

→  \(\frac{3069}{3} = 1-4^n\)

→ \(1024 = 4^n\)

→    \(4^n = 4^{5}\)

→     \(n = 5\)

Thus the above answer is correct.      

Learn more about Geometric series here:

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