Related InterviewSolutions

• If a, b, c are in GP, prove that (a2 + b2 ), (ab + bc), (b2 + c2 ) are in GP.
• If \(\frac{a + bx}{a - bx} = \frac{b +cx}{b-cx} = \frac{c+dx}{c- dx}\) (x \(\neq\) 0) then show that a, b, c and d are in G.Pa+bx /a - bx = b + cx/b - cx = c + dx/ c - dx (x ≠ 0)
• In a finite GP, prove that the product of the terms equidistant from the beginning and end is the product of first and last terms.
• If a, b, c, d are in G.P., prove that (a2 + b2 + c2), (ab + bc + cd), (b2 + c2 + d2) are in G.P.
• Six positive numbers are in G.P. such that their product is 1000. If the fourth term is 1, then find the last term.
• Find the sum to n terms of the series, 7 + 77 + 777 + ...... .
• What is the sum of n terms of the series 0.2 + 0.22 + 0.222 + ......?
• Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is \(\frac{3}{4}\) , then(a) a = 2, r = \(\frac{1}{2}\) (b) a = 2, r = \(\frac{3}{8}\) (c) a = 1, r = \(\frac{3}{4}\)(d) None of these
• If logxa, ax/2 and logb x are in G.P., then write the value of x.
• If pth, qth and rth terms of a G.P. are x, y, z respectively, then write the value of xq-r yr-p zp-q.