Question
Download Solution PDFFind the sum of the G.P.:
8/7, 8/49, 8/343, 8/2401, … to n terms.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The G.P. series is: 8/7, 8/49, 8/343, 8/2401, … to n terms
First term (a) = 8/7
Common ratio (r) = 1/7
Number of terms (n) = n
Formula used:
Sum of G.P. to n terms: Sn = a × (1 - rn) / (1 - r)
Calculations:
Sn = (8/7) × (1 - (1/7)n) / (1 - 1/7)
⇒ Sn = (8/7) × (1 - (1/7)n) / (6/7)
⇒ Sn = (8/7) × (7/6) × (1 - (1/7)n)
⇒ Sn = 8/6 × (1 - (1/7)n)
⇒ Sn = 4/3 × (1 - (1/7)n)
∴ The correct answer is option (4).
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