10th Maths Chapter-2 Formulas

UNIT - 2 : NUMBERS AND SEQUENCES

1	Euclid's Division Algorithm	a = bq + r
2	The terms of an AP (General form)	a, a+d, a+2d, a+3d, ......
3	To find nth term of an Arithmetic Progression (AP)	tn = a + (n - 1)d
4	To find the Number of terms	n = l - a⁄d + 1
5	Common difference	d = t2 - t1
6	Sum of terms of an A.P.	Sn = n⁄2 [2a + (n - 1)d] Sn = n⁄2 (a + l)
7	3 Consecutive terms of an AP	a-d, a, a+d
8	The terms of a GP (General form)	a, ar, ar2, ar3, ...
9	To find nth term of a Geometric Progression (G.P.)	tn = arn-1
10	Common ratio	r = t2⁄t1
11	Sum of n terms of a G.P.	Sn = a(rn - 1)⁄ r - 1
12	3 Consecutive terms of a GP	a/r, a, ar
13	Sum of infinite terms of a G.P.	S∞ = a⁄1 - r
14	Sum of first n natural numbers	Sn = n(n+1)⁄2
15	Sum of squares of first n natural numbers	Sn = n(n+1)(2n+1)⁄6
16	Sum of cubes of first n natural numbers	Sn = ( n(n+1)⁄2 )2
17	Sum of first n odd numbers	Sn = n2

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