Find the sum of the first 18 terms of the progression 3, 6, 12......

  • A 3(2\(^{17}\) - 1)
  • B 3(2\(^{18}\) - 1)
  • C 3(2\(^{18}\)+ 1)
  • D 3(2\(^{17}\) - 1)
jamb 1990mathematics

The correct answer is B. 3(2\(^{18}\) - 1)

The given progression is a geometric progression with first term a = 3 and common ratio r = 2. 

The sum of the first \(n\) terms of a geometric progression is given by the formula:
\(S_n = \frac{a(r^n - 1)}{r - 1}\). 

Substituting the values of a, r, and n = 18, we get:

\(S_{18} = \frac{3(2^{18} - 1)}{2 - 1} = 3(2^{18} - 1)\). 

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