Question

i was absent to progressions class plz any body explain in easy way so i can do my problems easily plzzzz frnds help me....

Answer 1

Arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is always constant.
For example: 1,3,5,7,9,11.....; 16,13,10,7....

In 1,3,5,7,9,11.....,
first term = 1
common difference = 3-1 = 2

in 16,13,10,7.....
first term = 16
common difference = 13-16 = -3

you can find the common difference by subtracting any two consecutive number. Given the first term(a) and the common difference(d), you can calculate the nth term of the AP($a_n$) and sum of n terms of the AP($S_n$).

$a_n=a+(n-1)d$

$S_n= \frac{n}{2}[2a+(n-1)d] =\frac{n}{2}[a+a_n]$