If the sum of an infinite GP is 10 and the common ratio is 1/3, what is the firs

₹0.0

Question: If the sum of an infinite GP is 10 and the common ratio is 1/3, what is the first term?

Options:

Correct Answer: 20

Solution:

The sum of an infinite GP is given by S = a / (1 - r). Here, S = 10 and r = 1/3. Thus, 10 = a / (1 - 1/3) = a / (2/3) => a = 10 * (2/3) = 20.

If the sum of an infinite GP is 10 and the common ratio is 1/3, what is the first term?

If the sum of an infinite GP is 10 and the common ratio is 1/3, what is the first term?

Step 1: Understand that we are dealing with an infinite geometric progression (GP) where the sum is given by the formula S = a / (1 - r).
Step 2: Identify the values given in the problem. We know the sum S = 10 and the common ratio r = 1/3.
Step 3: Substitute the known values into the formula: 10 = a / (1 - 1/3).
Step 4: Calculate (1 - 1/3). This simplifies to (2/3).
Step 5: Now rewrite the equation: 10 = a / (2/3).
Step 6: To solve for a, multiply both sides of the equation by (2/3): a = 10 * (2/3).
Step 7: Calculate 10 * (2/3). This gives a = 20.

Geometric Progression (GP) – Understanding the formula for the sum of an infinite geometric series and how to manipulate it to find the first term.
Common Ratio – Recognizing the significance of the common ratio in determining the behavior of the series.