Chapter 9 Sequences and Series Ex 9.1 Solutions
Question - 1 : - Write the first five terms of each of the sequences in Exercises 1 to 6 whose nth terms are:an = n (n + 2)
Answer - 1 : -
Given,
nth termof a sequence an = n (n + 2)
On substituting n =1, 2, 3, 4, and 5, we get the first five terms
a1 =1(1 + 2) = 3
a2 =2(2 + 2) = 8
a3 =3(3 + 2) = 15
a4 =4(4 + 2) = 24
a5 =5(5 + 2) = 35
Hence, the requiredterms are 3, 8, 15, 24, and 35.
Question - 2 : - an = n/n+1
Answer - 2 : -
Given nth term,an = n/n+1
On substituting n =1, 2, 3, 4, 5, we get
Hence, the requiredterms are 1/2, 2/3, 3/4, 4/5 and 5/6.
Question - 3 : - an = 2n
Answer - 3 : -
Given nth term, an =2n
On substituting n =1, 2, 3, 4, 5, we get
a1 = 21 =2
a2 = 22 =4
a3 = 23 =8
a4 = 24 =16
a5 = 25 =32
Hence, the requiredterms are 2, 4, 8, 16, and 32.
Question - 4 : - an = (2n – 3)/6
Answer - 4 : -
Given nth term, an =(2n – 3)/6
On substituting n =1, 2, 3, 4, 5, we get
Hence, the requiredterms are -1/6, 1/6, 1/2, 5/6 and 7/6..
Question - 5 : - an = (-1)n-1 5n+1
Answer - 5 : -
Given nth term,an = (-1)n-1 5n+1
On substituting n =1, 2, 3, 4, 5, we get
Hence, the requiredterms are 25, –125, 625, –3125, and 15625.
Question - 6 : - 
Answer - 6 : -
On substituting n =1, 2, 3, 4, 5, we get first 5 terms
Hence, the requiredterms are 3/2, 9/2, 21/2, 21 and 75/2.
Question - 7 : - Find the indicated terms in each of the sequences in Exercises 7 to 10whose nth terms are:
an = 4n – 3; a17, a24
Answer - 7 : -
Given,
nth term of the sequence is an = 4n – 3
On substituting n =17, we get
a17 =4(17) – 3 = 68 – 3 = 65
Next, onsubstituting n = 24, we get
a24 =4(24) – 3 = 96 – 3 = 93
Question - 8 : - Find the indicated terms in each of the sequences in Exercises 7 to 10whose nth terms are:
an = n2/2n ; a7
Answer - 8 : -
Given,
nth term of the sequence is an = n2/2n
Now, onsubstituting n = 7, we get
a7 = 72/27 =49/ 128
Question - 9 : - Find the indicated terms in each of the sequences in Exercises 7 to 10whose n_th terms are:
Answer - 9 : -
Given,
nth term of the sequence is an = (-1)n-1 n3
On substituting n =9, we get
a9 =(-1)9-1 (9)3 = 1 x 729 = 729
Question - 10 : - Find the indicated terms in each of the sequences in Exercises 7 to 10whose n_th terms are:
Answer - 10 : -
On substituting n =20, we get
