Question
Download Solution PDFFind the sum of the G.P.:
4/7, 4/49, 4/343, 4/2401, ... to n terms.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
G.P. = 4/7, 4/49, 4/343, 4/2401,... up to n terms
First term (a) = 4/7
Common ratio (r) = 1/7
Number of terms = n
Formula used:
Sum of n terms of G.P., Sn = a(1 - rn) / (1 - r), where |r| < 1
Calculation:
Sn = (4/7)[1 - (1/7)n] / (1 - 1/7)
⇒ Sn = (4/7)[1 - (1/7)n] / (6/7)
⇒ Sn = (4/7 × 7/6)[1 - (1/7)n]
⇒ Sn = (2/3)[1 - (1/7)n]
∴ The correct answer is option (1).
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