Tricks & tips, Short codes for Arithmetic Progression (AP) Quantitative Aptitude Study Materials for SSC, UPSC, PSC
AP is the short form of Arithmetic Progression. If you know the formulas in Arithmetic Progression you can simply solve the questions related to Arithmetic Progression, in the exams like SSC, UPSC, PSC etc. You can expect at least one question from Arithmetic Progression in the Quantitative Aptitude Section.
Consider an Arithmetic Progression a1, a2, a3, a4, .........
a= first term, here a=a1
d= difference between two adjacent numbers in an arithmetic progression
d= a2-a1 = a3-a2 = a4-a3
then n'th term Tn= a1+(n-1)d
Sum of first n numbers, Sn= n/2[ 2a+(n-1)d]
or
Sn = n/2[first term + last term]
Sum of first n natural numbers are, Sn= [n(n+1)]/2
Sum of squares of first n natural numbers, Sn Σn² = [n(n+1)(n+2)]/6
Sum of cubes of first n natural numbers, Sn Σn³ = [n² (n+1)² ]/4
= (Σn²)²
Sum of first n odd numbers, Sn = n²
Sum of first n even numbers, Sn = n(n+1)
If you have any doubts regarding divisibility of a number please feel free to ask through the commenting system
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