సిరీస్ మొత్తాన్ని కనుగొనండి : (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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ఇచ్చిన:

(20 + 22 + 24 +........+28) × 3

వాడిన ఫార్ములా:

ఇది ఒక రేఖాగణిత పురోగతి.

a = మొదటి పదం, r = సాధారణ నిష్పత్తి

జ్యామితీయ పురోగమనం మొత్తం = [a(r n - 1)/(r - 1)]

లెక్కింపు:

a = 1

r = (22/20) = 4/1 = 4

⇒ శ్రేణి మొత్తం = [1 × (45 - 1)/(4 - 1)] × 3

⇒ శ్రేణి మొత్తం = [1 × (210 - 1)/(3)] × 3

⇒ శ్రేణి మొత్తం = [1 × (1024 - 1)]

⇒ శ్రేణి మొత్తం = [1 × (1023)]

⇒ శ్రేణి మొత్తం = 1023

∴ సిరీస్ మొత్తం 1023.

ప్రత్యామ్నాయ పద్ధతి

(20 + 22 + 24 +........+28) × 3

⇒ (1 + 4 + 16 + 64 + 256) × 3

⇒ 341 × 3 = 1023

∴ సిరీస్ మొత్తం 1023.

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