Find the sum of 4 terms in a GP, given first term is 16 and common ratio is 6.

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Question

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UP Police SI (दरोगा) Official PYP (Held On: 2nd Dec 2021 Shift 1)

Answer 1

Given:

The sum of 4 terms in a GP, given first term is 16 and common ratio is 6.

Formula used:

The progression of the form is a, ar, ar², ar³, ......... Is known as geometric progression (where, a is the first term, and r is the common ratio)

Sum of n terms of G.P., Sn = \(\dfrac{a(r^n-1)}{(r-1)}\), where r > 1

Calculations:

Now, a = 16, r = 6, n = 4

Sn = \(\dfrac{16 × (6^4 - 1)}{(6 - 1)}\)

⇒ \(\dfrac{16 × (1296 - 1)}{(6 - 1)}\)

⇒ \(\dfrac{16 × 1295}{5}\) = 16 × 259 = 4144

Sn = 4144

∴ The answer is 4144

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