The second, the first and the third term of an A.P whose common difference is non zero form a G.P in that order. Find its common ratio. Answer: -2 Explanation: Let the terms in GP be a, ar, ar2. Hence the terms ar, a and ar2 are in AP. Therefore, a – ar = ar2– a ‘a’ cannot be 0. Hence, 1 – r = r2 – 1 r2 + r -2 = 0 (r + 2)(r – 1) = 0 Now r cannot be ‘1’ … [Read more...] about Arithmetic and Geometric Progressions
GRE Progressions
Sequences Series – nth term
Find the 50th term of the following series: 1 + 3 + 7 + 13 + 21 + ............ Answer: 2451 Explanation t2 – t1= 2 (2*1) t3 – t2= 4 (2*2) t4 – t3 = 6 (2*3) ……………………….. ………………………… ……………………….. t50 – t49= 98 (2*49) Adding all the equations, we get t50 – t1= 2 + 4 + 6 + ………. + 98 t50 – t1= 2450 t50 – 1 = 2450 Therefore, t50 = 2451 … [Read more...] about Sequences Series – nth term
Geometric Sequence – Triangles
One side of an equilateral triangle is 2 cms. The mid-points of its sides are joined to form another triangle whose mid-points are joined to form still another triangle. This process continues indefinitely. (i) Find the sum of the perimeters of all the triangles. (a) Cannot be determined (b) 4 (c) 12 (d) 8 (e) 10 Bonus Question (ii) Find the sum of the areas … [Read more...] about Geometric Sequence – Triangles