Arithmetico-geometric Sequence

Find the sum of n terms of the arithmetic- geometric sequence.

The sum of the infinite Arithmetico -Geometric progression3,4,4,… is _________.

If in a /_\ ABC the altitude from the vertices A,B,C on opposite side are in H.P. then sinA,sinB,sinC are in (A) H.P. (B) Arithmetico-Geometric progression (C) A.P. (D) G.P.

Which term of the geometric sequence: 1/4, -1/2, 1,….. Is 64?

If sin x,sin^(22)x and cos x.sin4x form an increasing geometric sequence,find the numerical value of cos2x. Also find the common ratio of geometric sequence.

Which term of the geometric sequence: 2sqrt(3),6,6sqrt(3),…..is 1458?

Let h_(n) and g_(n) be harmonic and geometric sequences respectively. If h_(1) = g_(1) = 1/2 and h_(10) = g_(10) = (1)/(1024) then

Which term of the geometric sequences, (i) 2,8,32,....... is 131072? (ii) sqrt(3),3,3sqrt(3),……..is 729? (iii) 1/3,1/9,1/27…………….. is 1/19683 ?

Find the sum of the infinite geometric sequence (1)/(2),(1)/(4),(1)/(8),......

Let A_6 be the sum of first six terms of an arithmetic sequence, and G_6 be the sixth term of a geometric sequence. Both sequences have the same first term, and the common difference of the arithmetic sequence equals the common ratio of the geometrical sequence, which is equal to two. If A_6/G_6=1/2, then G_6 - A_6 equals (i)1 (ii)3 (iii)48 (iv)144