If the first term of a geometric progression is 7 and the common ratio is 1/2, w

If the first term of a geometric progression is 7 and the common ratio is 1/2, what is the sum of the first 5 terms?

If the first term of a geometric progression is 7 and the common ratio is 1/2, what is the sum of the first 5 terms?

Step 1: Identify the first term (a) of the geometric progression, which is given as 7.
Step 2: Identify the common ratio (r) of the geometric progression, which is given as 1/2.
Step 3: Determine the number of terms (n) you want to sum, which is 5 in this case.
Step 4: Use the formula for the sum of the first n terms of a geometric progression: S_n = a(1 - r^n) / (1 - r).
Step 5: Substitute the values into the formula: S_5 = 7(1 - (1/2)^5) / (1 - 1/2).
Step 6: Calculate (1/2)^5, which is 1/32.
Step 7: Substitute this value back into the equation: S_5 = 7(1 - 1/32) / (1/2).
Step 8: Calculate 1 - 1/32, which is 31/32.
Step 9: Substitute this value into the equation: S_5 = 7(31/32) / (1/2).
Step 10: Dividing by (1/2) is the same as multiplying by 2, so S_5 = 7 * 31/32 * 2.
Step 11: Calculate 7 * 31 = 217, so S_5 = 217/32 * 2 = 434/32.
Step 12: Simplify 434/32 to get 14.

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