Arithmetic Progression (AP): General term and sum

Arithmetic Progression (AP): General term and sum An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutiv...

Arithmetic Progression (AP): General term and sum

An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive numbers is constant. This constant difference is known as the common difference.

General term:

The general term of an AP is given by the formula:

$T_n = a_1 + (n - 1)d$

where:

$T_n$ is the nth term in the AP
$a_1$ is the first term in the AP
$n$ is the position of the term in the AP
$d$ is the common difference between consecutive terms

Sum:

The sum of the first $n$ terms of an AP can be calculated using the formula:

$S_n = \frac{n}{2} (a_1 + a_n)$

where:

$S_n$ is the sum of the first n terms
$a_1$ is the first term in the AP
$a_n$ is the last term in the AP

Arithmetic Progression (AP): General term and sum

An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive numbers is constant. This constant difference is known as the common difference.

General term:

The general term of an AP is given by the formula:

$T_n = a_1 + (n - 1)d$

where:

$T_n$ is the nth term in the AP
$a_1$ is the first term in the AP
$n$ is the position of the term in the AP
$d$ is the common difference between consecutive terms

Sum:

The sum of the first $n$ terms of an AP can be calculated using the formula:

$S_n = \frac{n}{2} (a_1 + a_n)$

where:

$S_n$ is the sum of the first n terms
$a_1$ is the first term in the AP
$a_n$ is the last term in the AP

Arithmetic Progression (AP): General term and sum

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