Sequences and Series- Calculus

Sequences and Series- Calculus Sequence is a set of things 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. Sum of first p terms in of a sequence is Here i is the index of summation 1 is the lower limit and P is the upper limit Series is a number of things or events of similar type coming one after another. Example: A, AA, AAA, There are different types of sequences or progressions. Arithmetic Progression Geometric Progression Harmonic Progression A X H = G Here A stands for Arithmetic mean H stands for Harmonic mean and G stands for Geometric mean 1) Fourth and tenth terms in a arithmetic sequence are 48 and 36 respectively. Find the general term of the sequence. Answer: General term of Arithmetic sequence is tn = a + (n-1)d For fourth term n= 4 t4 = a + (4-1)d 48 = a+3d a = 48 3d For tenth term n = 10 t10 = a + (10-1)d 36 = a + 9d Substitute a = 48 3d in 36 = a+ 9d 36 = 48 3d + 9d 36 = 48 + 6d 6d = -12 d = -2 Substitute d = -2 in 48 = a+3d 48 = a + 3(-2) 48 = a -6 a = 54 General term t_n = 54 + (n-1)-2 tn = 54 -2n +2 tn = 56 2n