Sequence and series – Important Formulas for JEE Main 2026

1. n^th term of A.P : a +( n – 1)d where a is first terms, d is common difference , n is number of terms
2. n^th term of G.P : ar^{n – 1} where a first term, r is common ratio
3. n^th term of AGP : ( a + (n – 1)d) r^{n – 1}
4. n^th term of Diff in A.P : an² + bn + C
5. n^th term of Diff in G.P : abⁿ + C
6. n^th term of H.P : $\frac{1}{a + (n -1)d}$
7. a_n = T_n

Arithmetic Progression :

8. Sum of n terms of an A.P or S_n = $\frac{n}{2}$( 2a + (n -1)d) = $\frac{n}{2}$( a + l)

9. t₁ + t_n = t₂ + t_{n – 1} = t₃ + t_{n – 2} = …………….

10. Three terms in A.P $\rightarrow$ a – d, a, a + d

11. Four terms in A.P $\rightarrow$ a – 3d, a – d, a + d, a + 3d

12. a, b, c in A.P $\rightarrow$ 2b = a + c

13. a, b, c, d in A.P $\rightarrow$ a = l, b = l +m, c = l + 2m, d = l + 3m

14. AM of a₁, a₂, a₃,…………………… a_n is $\frac{a_1 + a_2 + a_3 + a_4+ ……..+a_n}{n}$

15. Inserting n AM’s between a and b $\rightarrow$ a, A₁, A₂,……………………. A_n, b are in A.P $\rightarrow$ d = $\frac{b – a}{n + 1}$, A_p = a + $\frac{p( b – a)}{n + 1}$

16. Sum of all n AM’s = $\frac{n}{2}$( a +b)

Harmonic Progression :

17. S_n – no formula

18. Three terms in H.P $\rightarrow$ $\frac{1}{a – d}$, $\frac{1}{a}$, $\frac{1}{a + d}$

19. Four terms in H.P $\rightarrow$ $\frac{1}{a – 3d}$ , $\frac{1}{a – d}$ , $\frac{1}{a + d}$ , $\frac{1}{a + 3d}$

20. a, b, c are in H.P $\rightarrow$ $\frac{2}{b}$ = $\frac{1}{a}$ + $\frac{1}{c}$

21. HM of a₁, a₂, a₃ …………… a_n is $\frac{n}{1/a_1 + 1/a_2 + 1/a_3+ ….. 1/a_n}$