Solve the Following Question.(4 Marks)

Question 14 Marks

Find the sum of infinite terms of $1+\frac{4}{5}+\frac{7}{25}+\frac{10}{125}+\frac{13}{625}+\ldots$

Question 24 Marks

Find Sn of the following arithmetico-geometric sequences. : 3, 12, 36, 96, 240, ……

Question 34 Marks

Find Sn of the following arithmetico-geometric sequences. : 1, 2 × 3, 3 × 9, 4 × 27, 5 × 81, ……

Question 44 Marks

Find Sn of the following arithmetico-geometric sequences..

$1,4 x, 7 x^2, 10 x^3, 13 x^4$

Question 54 Marks

Find Sn of the following arithmetico-geometric sequences.

$2,4 x, 6 x^2, 8 x^3, 10 x^4, \ldots \ldots$

Question 64 Marks

If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by $\frac{18}{5}$, find the
numbers.

Question 74 Marks

If $S_n, S_{2 n}, S_{3 n}$ are the sum of $n, 2 n, 3 n$ terms of a G.P. respectively, then verify that $S_n\left(S_{3 n}-\right.$

$\left.S_{2 n}\right)=\left(S_{2 n}-S_n\right)^2$

Question 84 Marks

If S, P, R are the sum, product, and sum of the reciprocals of n terms of a G.P, respectively,

then verify that $\left[\frac{S}{R}\right]^n= P ^2$.

Maths Solve the Following Question.(4 Marks)