Math 5

Arithmetic Progression

1.  a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d

2.  d = a₂ – a₁ = a₃ – a₂ = ……. = a_n – a_{n – 1}

 

1. nth Term of an AP:-   a_n = a + (n − 1) × d

2. Sum of N Terms of AP:-     S_n = n/2[2a + (n − 1) × d]

3. Sum of AP when the Last Term is Given:-     S  = n/2 (first term + last term)

 

Geometric Progression

 a, ar, ar², ar³, ar⁴,…, ar^n-1

1. Nth Term of G.P:-    a_n = t_n = ar^n-1

2. Sum of N term of GP:-   S_n = a[(rⁿ – 1)/(r – 1)] if r ≠ 1 and r > 1

3.  S_n = na if r = 1

4. S_n = a[(rⁿ – 1)/(r – 1)] if r ≠ 1 and r > 1 

 

Harmonic progression

 

Application of Calculus

Co-ordinate geometry