MATHS : Algebra & Arithmetical Process

� Algebra:

● Laws of Indices:
(i) am ∙ an = am + n
(ii) am/an
(iii) (am)n = amn
(iv) a0 = 1 (a ≠ 0).
(v) a- n = 1/an
(vi) n√am = am/n
(vii) (ab)m = am ∙ bn.
(viii) (a/b) m = am/bn
(ix) If am = bm (m ≠ 0), then a = b.
(x) If am = an then m = n.

● Arithmetical Progression (A.P.):

(i) The general form of an A. P. is a, a + d, a + 2d, a+3d,.....

where a is the first term and d, the common difference of the A.P.

(ii) The nth term of the above A.P. is tn = a + (n - 1)d.

(iii) The sum of first n terns of the above A.P. is s = n/2 (a + l) = (No. of terms/2)[1st term + last term] or, S = n/2 [2a + (n - 1) d]

(iv) The arithmetic mean between two given numbers a and b is (a + b)/2.

(v) 1 + 2 + 3 + ...... + n = [n(n + 1)]/2.

(vi) 12 + 22 + 32 +……………. + n2 = [n(n+ 1)(2n+ 1)]/6.

(vii) 13 + 23 + 33 + . . . . + n3 = [{n(n + 1)}/2 ]2.