In a geometric progression, if the first term is 5 and the common ratio is 0.5, what is the sum of the first 4 terms?
Practice Questions
1 question
Q1
In a geometric progression, if the first term is 5 and the common ratio is 0.5, what is the sum of the first 4 terms?
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The sum of the first n terms of a GP is given by S_n = a(1 - r^n) / (1 - r). Here, S_4 = 5(1 - 0.5^4) / (1 - 0.5) = 5(1 - 0.0625) / 0.5 = 5 * 0.9375 / 0.5 = 9.375.
Questions & Step-by-step Solutions
1 item
Q
Q: In a geometric progression, if the first term is 5 and the common ratio is 0.5, what is the sum of the first 4 terms?
Solution: The sum of the first n terms of a GP is given by S_n = a(1 - r^n) / (1 - r). Here, S_4 = 5(1 - 0.5^4) / (1 - 0.5) = 5(1 - 0.0625) / 0.5 = 5 * 0.9375 / 0.5 = 9.375.
Steps: 10
Step 1: Identify the first term (a) and the common ratio (r) of the geometric progression. Here, a = 5 and r = 0.5.
Step 2: Determine the number of terms (n) you want to sum. In this case, n = 4.
Step 3: Use the formula for the sum of the first n terms of a geometric progression: S_n = a(1 - r^n) / (1 - r).
Step 4: Substitute the values into the formula: S_4 = 5(1 - 0.5^4) / (1 - 0.5).
Step 5: Calculate r^n: 0.5^4 = 0.0625.
Step 6: Substitute this value back into the equation: S_4 = 5(1 - 0.0625) / (1 - 0.5).
Step 7: Simplify the equation: S_4 = 5(0.9375) / 0.5.
Step 8: Calculate the numerator: 5 * 0.9375 = 4.6875.
Step 9: Divide by the denominator: 4.6875 / 0.5 = 9.375.
