Question
Download Solution PDFFind the sum of the G.P.:
1/5, 1/25, 1/125, 1/625, … to n terms.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
First term (a) = 1/5
Common ratio (r) = 1/25 ÷ 1/5 = 1/5
Number of terms (n) = n
Formula Used:
Sum of n terms of a G.P. = Sn = a × (1 - rn) / (1 - r), where |r| < 1
Calculation:
Substitute the values:
⇒ Sn = (1/5) × (1 - (1/5)n) / (1 - 1/5)
⇒ Sn = (1/5) × (1 - (1/5)n) / (4/5)
⇒ Sn = (1 - (1/5)n) / 4
⇒ Sn = 1/4 × (1 - (1/5)n)
Final Answer:
The sum of the given G.P. up to n terms is: 1/4(1 - (1/5)n).
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