Question
Download Solution PDFFind the sum of the G.P.:
5/4,5/16,5/64,5/256,… to n terms.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
G.P. series: 5/4, 5/16, 5/64, 5/256, ... up to n terms
Formula used:
Sum of n terms of G.P. = a × (1 - rn) ÷ (1 - r), where |r| < 1
Calculations:
First term (a) = 5/4
Common ratio (r) = (5/16) ÷ (5/4) = 1/4
Sum = (5/4) × (1 - (1/4)n) ÷ (1 - 1/4)
= (5/4) × (1 - (1/4)n) ÷ (3/4)
= (5/4) × (4/3) × (1 - (1/4)n)
= (5/3) × (1 - (1/4)n)
∴ Sum of n terms = (5/3) × (1 - (1/4)n)
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