Chapter 9 Sequences and Series Ex 9.1 Solutions
Question - 11 : - Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:a1┬а= 3, an┬а= 3an-1┬а+ 2for all n > 1
Answer - 11 : -
Given, an┬а=3an-1┬а+ 2 and a1┬а= 3
Then,
a2┬а=3a1┬а+ 2 = 3(3) + 2 = 11
a3┬а=3a2┬а+ 2 = 3(11) + 2 = 35
a4┬а=3a3┬а+ 2 = 3(35) + 2 = 107
a5┬а=3a4┬а+ 2 = 3(107) + 2 = 323
Thus, the first 5terms of the sequence are 3, 11, 35, 107 and 323.
Hence, thecorresponding series is
3 + 11 + 35 + 107 +323 тАжтАж.
Question - 12 : - Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:a1┬а= -1, an┬а= an-1/n, n тЙе 2
Answer - 12 : -
Given,
an┬а= an-1/nand a1┬а= -1
Then,
a2┬а= a1/2= -1/2
a3┬а= a2/3= -1/6
a4┬а= a3/4= -1/24
a5┬а= a4/5= -1/120
Thus, the first 5terms of the sequence are -1, -1/2, -1/6, -1/24 and -1/120.
Hence, thecorresponding series is
-1 + (-1/2) + (-1/6) +(-1/24) + (-1/120) + тАжтАж.
Question - 13 : - Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:a1┬а= a2┬а= 2, an┬а= an-1┬атАУ1, n > 2
Answer - 13 : -
Given,
a1┬а= a2,an┬а= an-1┬атАУ 1
Then,
a3┬а= a2┬атАУ1 = 2 тАУ 1 = 1
a4┬а= a3┬атАУ1 = 1 тАУ 1 = 0
a5┬а= a4┬атАУ1 = 0 тАУ 1 = -1
Thus, the first 5terms of the sequence are 2, 2, 1, 0 and -1.
The correspondingseries is
2 + 2 + 1 + 0 + (-1) +тАжтАж
Question - 14 : - The Fibonacci sequence is defined by
1 = a1┬а= a2┬аand an┬а= anтАУ 1┬а+ an тАУ 2, n > 2
Find an+1/an, for n = 1, 2, 3, 4, 5┬а
Answer - 14 : -
Given,
1 = a1┬а=a2
an┬а= anтАУ 1┬а+ an тАУ 2, n > 2
So,
a3┬а= a2┬а+a1┬а= 1 + 1 = 2
a4┬а= a3┬а+a2┬а= 2 + 1 = 3
a5┬а= a4┬а+a3┬а= 3 + 2 = 5
a6┬а= a5┬а+a4┬а= 5 + 3 = 8
Thus,
