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1
Sum of first n terms in an A.P.
$$\dfrac{n}{2}[2a + (n-1)d]$$
2
Sum of first n terms in a G.P.
$$\dfrac{a(r^n-1)}{r-1}$$
3
Sum to infinite terms in a G.P.
$$\dfrac{a}{1-r}$$
4
Sum of first n terms in an A.G.P.
$$\displaystyle \dfrac{a-[a+(n-1)d]r^n}{1-r} + \dfrac{dr(1-r^{n-1})}{(1-r)^2}$$
5
Sum of infinite terms in an A.G.P.
$$\displaystyle \dfrac{a}{1-r} + \dfrac{dr}{(1-r)^2}$$
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