Question

Full form of Ap in maths

Answer 1

arithmetic progression

Answer 2

$\textbf{ \underline{Full form of AP = Arithmetic progression}}$

$\text{\underline {\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}$

$\textbf{ \underline{ \underline{ARITHMETIC PROGRESSION}}}$

A sequence $\text{a}_1,\text{a}_2,\text{a}_3,\text{a}_4.....\text{a}_ \text{n}$ is called an arithmetic progression . If there exists a constant number $\textbf{d}$ such that

$\text{a}_2 = \text{a}_1 + \text{d} \\ \text{a}_3 = \text{a}_2 + \text{d} \\ \text{a}_4 = \text{a}_3 + \text{d} \\ . \: \: \: \: \: \: \: \: \: \: \: \: . \\ . \: \: \: \: \: \: \: \: \: \: \: \: . \\ . \: \: \: \: \: \: \: \: \: \: \: \: . \\ \text{a}_ \text{n} = \text{a}_\text{n - 1} + \text{d} (\text{ and \: so \: on}$

The constant $\textbf{d}$ is called the common difference of the AP .

Thus, If the first term is $\textbf{a}$ and the common difference is $\textbf{d}$, then

$\text{a}, \: \text{a + d}, \: \text{a +2 d}, \: \text{a + 3d}, \: \text{a + 4d},....$

is an arithmetic progression.