Tips and Tricks and Shortcuts for AP and GP And HP

Tips and Tricks for AP

1. nth term of an AP = t_n= a + (n – 1)d
2. Number of terms of an AP (n) = [ \frac{(l-a)}{d} ]+ 1
3. Sum of first n terms in an AP = S_n = \frac{n}{2} [2a + (n − 1) d] OR  \frac{n}{2}  (a+l)
4. While Solving three unknown Term in an A.P whose sum or product is given should be assumed as a-d, a, a+d.
5. While Solving Four terms in an A.P. whose sum or product is given should be assumed as a-3d, a-d, a+d, a+3d.

Tips and Tricks for GP

1. nth term of an GP =  a_n= ar^n-1
2. Sum of first n terms in an GP = S_n = = a \times \frac{r^{n} -1}{r-1} if r>1
3. Sum of first n terms in an GP = S_n = = a \times \frac{1-r^{n}}{1-r} if r<1

4. Infinite term GP \frac{a}{1-r}

5. While Solving three unknown Term in an G.P whose sum or product is given should be assumed as (\frac{a}{r}),  a,  ar

Tips and Tricks for HP

1. nth term of an HP = a_{n} = \mathbf{\frac{1}{(a + (n – 1)d)}}
2. Harmonic Mean of two numbers a and b is \mathbf{\frac{2ab}{a+b}}
3. While Solving HP Questions we convert given Problem in an AP.