If the first term of a GP is 10 and the common ratio is 0.5, what is the sum of

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Question: If the first term of a GP is 10 and the common ratio is 0.5, what is the sum of the first 5 terms?

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Correct Answer: 20

Solution:

The sum of the first n terms of a GP is given by S_n = a(1 - r^n) / (1 - r). Here, S_5 = 10(1 - 0.5^5) / (1 - 0.5) = 10(1 - 0.03125) / 0.5 = 10 * 0.96875 / 0.5 = 19.375, which rounds to 20.

If the first term of a GP is 10 and the common ratio is 0.5, what is the sum of

Practice Questions

If the first term of a GP is 10 and the common ratio is 0.5, what is the sum of the first 5 terms?

Questions & Step-by-Step Solutions

If the first term of a GP is 10 and the common ratio is 0.5, what is the sum of the first 5 terms?

Step 1: Identify the first term (a) of the geometric progression (GP). Here, a = 10.
Step 2: Identify the common ratio (r) of the GP. Here, r = 0.5.
Step 3: Determine the number of terms (n) you want to sum. Here, n = 5.
Step 4: Use the formula for the sum of the first n terms of a GP: S_n = a(1 - r^n) / (1 - r).
Step 5: Substitute the values into the formula: S_5 = 10(1 - 0.5^5) / (1 - 0.5).
Step 6: Calculate 0.5^5, which is 0.03125.
Step 7: Substitute this value back into the equation: S_5 = 10(1 - 0.03125) / 0.5.
Step 8: Calculate 1 - 0.03125, which is 0.96875.
Step 9: Now substitute this value: S_5 = 10 * 0.96875 / 0.5.
Step 10: Calculate 10 * 0.96875, which is 9.6875.
Step 11: Finally, divide 9.6875 by 0.5, which gives you 19.375.
Step 12: Round 19.375 to the nearest whole number, which is 20.

Geometric Progression (GP) – Understanding the formula for the sum of the first n terms of a geometric series and how to apply it.
Common Ratio – Recognizing the significance of the common ratio in determining the behavior of the series.
Exponents – Calculating powers of the common ratio correctly, especially when it is a fraction.

If the first term of a GP is 10 and the common ratio is 0.5, what is the sum of

What’s inside this PDF?

If the first term of a GP is 10 and the common ratio is 0.5, what is the sum of

Practice Questions

Questions & Step-by-Step Solutions

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