Greetings friends

l

i decided to create a list of all formulas regarding arithmetic progression, number of terms, sums etc all in one post. i may have some questions and or inaccuaracies, so you are welcome to correct me or just say hi

1. HOW TO FIND NUMBER OF TERMS \(x_n = a+d (n-1)\)

\(n\) = # of term

\(a\) = first term

\(d\) = distance

Example: a= 3

d = 5

Question: find the 9th term

\(x_9 = 3+5 (n-1)\)

\(x_9 = 3+5 (n-1)\)

\(x_9 = 3+5n-5\)

\(x_9 = 5n-2\)

now plug in 9 into 5n-2

\(x_9 = 5*9-2 = 43\)

hence \(9th\) term is \(43\)

2. HOW TO FIND THE SUM OF TERMS SUM OF N TERMS = \(\frac{n}{2} (2a+(n-1)d)\)

Example\(a\) = 1 the first term

\(d\) = 3 distance

\(n\) = 10 how many terms to add up

Question: what is the sum of 10 terms with distance 3 and the first term 1 ?

\(\frac{10}{2} (2 *1 +(10-1)3)\)

\(= 5(2+9·3) = 5(29) = 145\)

3.HOW TO FIND THE SUM OF THE FIRST CONSECUTIVE NUMBERS \(\frac{n(n+1)}{2}\)

where \(n\) is number of terms

Example: what is the sum of the first 15 numbers ?

\(\frac{15(15+1)}{2}\) =\(238\)

4.HOW TO FIND THE SUM OF THE FIRST EVEN NUMBERS \(\frac{n(n+2)}{4}\)

where \(n\) is number of terms

\(\frac{15(15+2)}{4}\) = \(8\)

5. HOW TO FIND NUMBER OF TERMS FROM A TO B \(\frac{first..term +last..term}{2} +1\)

6. HOW TO FIND SUM OF ODD NUMBERS FROM A TO B Step one: \(find..the..number...of..terms\)

Step two: \(\frac{first..term+last..term}{2}\) \(* number..of.. terms\)

7. NUMBER OF MULTIPLES X IN THE RANGE \(\frac{last..multiple..of..x - first..multiple..of...x}{x}+1\)

Eg. how many multiples of 4 are there between 12 and 96?

\(\frac{96-12}{4}\)+1 = 22

to be continued

by the way I myself have question

what is the difference between this \(\frac{n(n+1)}{2}\) and this formula SUM OF N TERMS = \(\frac{n}{2} (2a+(n-1)d)\) ?

I will add more useful formulas later