2 + 22 + 23 + 24 + ..... + 28 = ?

This question was previously asked in
TSPSC VRO 2018 Official Paper
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  1. 510
  2. 1024
  3. 1018
  4. 1022

Answer (Detailed Solution Below)

Option 1 : 510
Free
TSPSC VRO: General Knowledge (Mock Test)
20 Qs. 20 Marks 12 Mins

Detailed Solution

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Given:

2 + 22 + 23 + 24 + ..... + 28 = ?

Formula used:

Sum of geometric series: {a × (r8 - 1)}/(r - 1)

Where,

a = first term, r = common ratio, n = number of terms

Calculation:

Here, a = 2, r = 2, and n = 8

S = 2 × {(28 - 1)}/(2 - 1)}

⇒ S = 2 × (256 - 1) / (2 - 1)

⇒ S = 2 × (255) / (1)

⇒ S = 2 × 255

⇒ S = 510

∴ The correct answer is option (1).

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