10th Maths 2nd lesson samacheer kalvi formula

2nd Lesson Sequence and series

Arithmetic Progression:

The first term of an A.P is generally denoted by ‘a’ and the common difference is denoted by‘d’.

t_n = a + (n-1) d

S_n =n/2 [2a + (n-1) d] = n/2[2a+l]

n = (l-a)/d +1

……….a, a+d, a+2d………..

………a-d, a, a+d…………. are A.P. numbers.

Geometric Progression:The first term of a G.P is generally denoted by ‘a’ and the common ratio is denoted by ‘r’.

t_n = a .r^n-1

S_n = a (rⁿ-1) / (r-1) if(r>1)

     = a (1-rⁿ) / (1-r) if (r <1)

…………a, ar, ar^{2………………}

…………a/r, a ar………… are G.P numbers.

  

Special series:

∑n = n(n+1)/2

∑n²  = n(n+1)(2n+1)/6

∑n³  = [n(n+1)/2]²