Sequences and Series

If $a, b, c$ are in Arithmetic Progression, which of the following is true?

Find $a_{50}$ for the sequence $a_n = (-1)^n \cdot 2$.

The formula for the sum of the first $n$ natural numbers is:

For a finite A.P. with first term $a$ and last term $l$, the arithmetic mean of all its terms is:

If $S_n$ is the sum of first $n$ terms of an A.P., then the $n^{th}$ term $a_n$ is given by:

The $10^{th}$ term of the A.P. $-1.2, -3.2, -5.2, ...$ is:

Find the sum to infinity of $1 + \frac{1}{2} + \frac{1}{4} + \dots$.

Find the $4^{th}$ term of the G.P. $x, 2x, 4x, \dots$.

Determine the geometric mean of $9$ and $9$.

If $a$ and $b$ are two positive numbers, the relationship $A = G$ holds if and only if:

If the Arithmetic Mean ($A$) of two numbers is $15$, then their sum $a + b$ is:

If the Geometric Mean ($G$) of two positive numbers is $6$, then their product $ab$ is:

What is the value of $\sum_{k=1}^{5} 4$?

If $a_n = 10n$, what is the sum of the first 2 terms?

Calculate the sum $\sum_{k=1}^{2} (k^3 - k)$.