can anyone give all the formulae of A.P., G.P , permutaion and combination

Hello student,
Please find the answer to your question below
1)An arithmetic progression is given by a, (a + d), (a + 2d), (a + 3d), ...
where a = the first term , d = the common difference
tn= a + (n – 1)d
where tn= nthterm, a= the first term , d= common difference
n=((l−a)/d)+1
where n = number of terms, a= the first term , l = last term, d= common difference
Sn=(n/2)[2a+(n−1)d]=(n/2)[a+l]
where a = the first term,d= common difference,l=tn=nthterm =a+(n−1)d
Tn= Sn- Sn-1
2)A Geometric Progression (G.P.) is given by a, ar, ar², ar³, ...
where a = the first term , r = the common ratio
tn=ar^n-1
where tn= nthterm, a= the first term , r = common ratio, n = number of terms
Sn=a(rⁿ-1)/(r-1) if r>1
=a(1-rⁿ)/(1-r) if r<1
S∞=a/(1−r) (if 0 < r < 1)
GM² = AM × HM
To solve most of the problems related to G.P., the terms of the G.P. can be conveiently taken as
3 terms :a/r, a, ar
5 terms :a/r²,a/r, a, ar, ar²

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