If the 3rd and 7th terms of a G.P are 9 and 1/9 respectiv...
If the 3rd and 7th terms of a G.P are 9 and 1/9 respectively. Find the common ratio.
\(\frac{1}{3}\)
\(\frac{1}{9}\)
\(\frac{2}{3}\)
\(\frac{2}{9}\)
Correct answer is A
\(T_n = ar^{n - 1}\) (terms of a G.P)
\(T_3 = ar^2 = 9\) ... (i)
\(T_7 = ar^6 = \frac{1}{9}\) ... (ii)
Divide (i) by (ii);
\(\frac{ar^6}{ar^2} = \frac{\frac{1}{9}}{9}\)
\(r^4 = \frac{1}{81}\)
\(r^4 = (\frac{1}{3})^4\)
\(r = \frac{1}{3}\)
In how many ways can 3 seats be occupied if 5 people are willing to sit?...
Find the values of x for which \( \frac{1}{2x^2 - 13x +15} \) is not defined,...
In the diagram, PQ and PS are tangents to the circle O. If PSQ = m, <SPQ = n and <SQR = 33\(^o...
Evaluate \(\int_1 ^2(6x^2-2x)dx\) ...
Find the sum of the first 18 terms of the series 3, 6, 9,..., 36. ...