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In a geometric progression, first term is 7, the last term is 448 and the sum is 889. The common ratio of the geometric progression is
1. 3/2
2. 2
3. 3
4. 3.5

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Best answer
Correct Answer - Option 2 : 2

Concept:

Geometric progression formulas for calculating nth term and sum of ‘n’ terms.

nth term of a geometric progression = ar(n - 1) ----(1)

Sum of ‘n’ terms of a geometric progression:

\(S_n=\frac{a(r^n-1)}{r-1}\) ----(2)

Where

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

Calculation:

Given:

a = 7, Last term(l) = 448, Sn = 889

Let n be the last term of GP;

From equation (1);

448 = 7r(n-1)

r(n-1) = 64

∴ rn = 64r ----(3)

From equation (2)

\(889=\frac{7(r^n-1)}{r-1}\)

\(\frac{(r^n-1)}{r-1}=127\)

From equation (3)

\(\frac{(64r-1)}{r-1}=127\)

64r - 1 = 127r - 127

63r = 126

r = 2

Note:

In terms of common ratio(r), first term, and Last term(l) sum of GP(Sn) is given as;

\(S_n=\frac{lr-a}{r-1}\)

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