Question

if the first term is 'a' and common difference is 'd' then the formula to calculate the sum of n terms of an arithmetic progression is ____​

Answer 1

AnswEr :

⠀

If the first term is 'a' and the Common difference is 'd' then the formula to calculate the sum of n terms of an Arithmetic Progression is ${\underline{\pmb{\red{\sf{\dfrac{n}{2}2a+(n -1)d}}}}}.$

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$\qquad\quad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\;Formulas\:\bigstar}}}}$

$\sf{1) \: n^{th}\; term\; of \: AP \: with \: Last \: term = a_n = a + \bigg\lgroup n - 1\bigg\rgroup d}$

$\sf{2) \;Sum \;of\;AP \;with\; Last \;term = S_n = \dfrac{n}{2}\bigg\lgroup a + l\bigg\rgroup}$

$\textsf{3) Form of AP = a, a + d, a + 2d, a + 3d...}$

• Basically, Arithmetic Progression (AP) is a sequence of term in order where the Common difference of any two terms will be Constant.

• To Calculate Common Difference 'd' of an AP (Arithmetic Progression) subtract second term from first term of the AP $\sf{a_2 - a_1 = d}.$

Answer 2

Given :-

If the first term is 'a' and common difference is 'd'

To Find :-

Formula to calculate the sum of n terms of an arithmetic progression is

Solution :-

The formula to calculate the sum of n terms of an arithmetic progression is

n/2 {2a + (n - 1)d}

Where

n = number of terms

a = First term

d = common difference