Question
Download Solution PDFFind the sum of the G.P. :
3/5 , 3/25 , 3/125 , 3/625 ,... to n terms.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The G.P. series is: 3/5, 3/25, 3/125, 3/625, ... to n terms.
First term (a) = 3/5
Common ratio (r) = 1/5
Number of terms (n) = n
Formula used:
Sum of G.P. for n terms, Sn = a \(\frac{1-r^n}{1-r}\), where |r| < 1
Calculation:
Sn = (3/5) \(\frac{1-(1/5)^n}{1-(1/5)}\)
⇒ Sn = (3/5) \(\frac{1-(1/5)^n}{4/5}\)
⇒ Sn = (3/5) × (5/4) × (1 - (1/5)n)
⇒ Sn = 3/4 (1 - (1/5)n)
∴ The correct answer is option 1.
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