Sequences and Series Tutors

Sequences and Series Tutors A sequence is a set thing in a certain order Example: 2, 4, 6 (Sequence of even numbers) A sequence contains list of values in an ordered way. All these values are called as terms. A finite sequence is that which contains a finite number of terms. a1, a2, ,an( n is some finite value) An infinite sequence is that which contains an infinite number of terms. a1, a2, ,an, ( n is an infinite number) Different types of sequences are Arithmetic sequence or progression (A.P) d Common difference A.P is of the form a, a+d, a+2d ....... l Last term Last term = tn = a + (n-1) d a First term Sum of n terms = 2a + (n-1)d or a + l n number of terms Geometric sequence (G.P) r common ratio G.P is of the form a, ar, ar..... Last term = tn = ar(n-1) Harmonic sequence (H.P) H.P is of the foxrm 1a , 1(a+d) , 1(a+2d), tn = 1(nth term of corresponding A.P) Harmonic mean of two terms a and b is 2ab(a+b). A X H = G Here A stands for Arithmetic mean H stands for Harmonic mean and G stands for Geometric mean Example: Find the first three terms of the sequence tn = (-2)n/( n+1) Answer: First term = n = 1 t1 = (-2)1/( 1+1) = (-2)/( 2) = -1 Second term = n = 2 t2 = (-2)2/( 2+1) = 4/( 3) Third term = n = 3 t3 = (-2)3/( 3+1) = (-8)/( 4) = -2 The first three terms are -1, 4/3, -2