Find the sum of the series : (20 + 22 + 24 +........+28) × 3

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SSC CGL Memory Based Test (Held On: 17 July 2023) (All Shifts)
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  1. 1023
  2. 1331
  3. 1024
  4. 923

Answer (Detailed Solution Below)

Option 1 : 1023
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Detailed Solution

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Given:

(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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