AP, GP and HP Shortcut, tricks, and tips

Here, are some easy tips and tricks for you to solve AP, GP and HP questions quickly, easily, and efficiently in competitive exams.

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.