The 4^th term of an AP is 13 while the 10^th term is 31. Find the 24^th term

$\begin{align}  & \text{The }nth\text{ term of the progression }\tfrac{4}{2},\tfrac{7}{3},\tfrac{10}{4},\tfrac{13}{4},\cdot \cdot \cdot \text{ is} \\ & (A)\text{ }\tfrac{3n-1}{n+1}\text{ }(B)\text{ }\tfrac{1-3n}{n+1}\text{ }(C)\text{ }\tfrac{3n+1}{n+1}\text{  (D) }\tfrac{3n+1}{n-1} \\\end{align}$

$\begin{align}  & \text{If the sum of the first term of G}\text{.P is 3, and the sum of the second  and} \\ & \text{the  third term is }-6,\text{ find the sum of the first term and the common ratio} \\ & \text{(A) 5 (B) }-2\text{  (C) }-3\text{  }(D)\text{ }-5 \\\end{align}$

The sum to infinity of a geometric progression is $-\tfrac{1}{10}$and the first term is $-\tfrac{1}{8}$.Find the common ratio of the progression.

The nth term of a sequence ${{n}^{2}}-6n-4$. Find the sum of the 3^rd and 4^th terms.

The second term of a geometric series is 4, while the fourth term is 16. Find the sum of the first five terms

Find the sum of the first 18 terms of the series 3, 6, 9, -, -, -, 36.

The 3^rd term of an arithmetic progression is  – 9 and the 7^th  term is –29. Find the 10^th term of the progression

Find the sum to infinity 0.5 + 0.05 + 0.005 +0.0005 +….

Find to infinity, the sum of the sequence $1,\tfrac{9}{10},{{(\tfrac{9}{10})}^{2}},{{(\tfrac{9}{10})}^{3}}\cdot \cdot \cdot $