Sum of First n Terms in GP

What is a geometric progression?

• A geometric progression is a sequence where each term is obtained by multiplying the previous term by a constant ratio.

• A geometric progression is a series of random numbers without any specific pattern.

• A geometric progression is a sequence where each term is the sum of the previous term and a constant.

• A geometric progression is a sequence where each term is divided by a constant ratio.

How do you find the sum of the first n terms in a GP?

• S_n = a * (1 - r^n) / (1 - r) for r ≠ 1; S_n = n * a for r = 1.

• S_n = a * (r^n - 1) / r for r ≠ 1

• S_n = a * r^n / (1 - r) for r ≠ 1

• S_n = a + r * n for r = 1

If the first term is 2 and the common ratio is 3, what is the sum of the first 4 terms?

• 80

• 100

• 40

• 60

What is the formula for the sum of the first n terms of a geometric series?

• S_n = a(1 + r^n) / (1 + r)

• S_n = a + ar + ar^2 + ... + ar^(n-1)

• S_n = a(1 - r^n) / (1 - r)

• S_n = ar^n / (1 - r)

If a = 5 and r = 2, what is S_3?

• 30

• 25

• 40

• 35

How does the common ratio affect the sum of the series?

• The common ratio only determines the first term of the series.

• The common ratio affects the speed of convergence but not the sum.

• The common ratio has no effect on the sum of the series.

• The common ratio affects whether the series converges or diverges, influencing the sum.

Calculate the sum of the first 5 terms of a GP with a = 1 and r = 4.

• 341

• 250

• 100

• 500

What happens to the sum as n approaches infinity if r < 1?

• The sum diverges to infinity.

• The sum oscillates indefinitely.

• The sum approaches a finite value.

• The sum becomes negative.

If the first term is 10 and the common ratio is 0.5, what is the sum of the first 6 terms?

• 30.0

• 25.0

• 15.5

• 19.6875

Explain why the sum of a GP diverges when r > 1.

• The sum of a GP diverges only when r = 1.

• The sum of a GP diverges when r > 1 because the terms increase indefinitely.

• The sum of a GP is always finite regardless of r.

• The sum of a GP converges when r > 1.