Question
Download Solution PDFFind the sum of the series : (20 + 22 + 24 +........+28) × 3
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
(20 + 22 + 24 +........+28) × 3
Formula Used:
It is a Geometric Progression.
a = first term, r = common ratio
Sum of the Geometric Progression = [a(rn - 1)/(r - 1)]
Calculation:
a = 1
r = (22/20) = 4/1 = 4
⇒ Sum of the series = [1 × (45 - 1)/(4 - 1)] × 3
⇒ Sum of the series = [1 × (210 - 1)/(3)] × 3
⇒ Sum of the series = [1 × (1024 - 1)]
⇒ Sum of the series = [1 × (1023)]
⇒ Sum of the series = 1023
∴ The Sum of the series is 1023.
Alternate Method
(20 + 22 + 24 +........+28) × 3
⇒ (1 + 4 + 16 + 64 + 256) × 3
⇒ 341 × 3 = 1023
∴ The Sum of the series is 1023.
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