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