Arithmetic Progressions
Exercise 5.2
Question 1
Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the A.P.
a
|
d
|
n
|
an
| |
I
|
7
|
3
|
8
|
…...
|
II
|
− 18
|
…..
|
10
|
0
|
III
|
…..
|
− 3
|
18
|
− 5
|
IV
|
− 18.9
|
2.5
|
…..
|
3.6
|
V
|
3.5
|
0
|
105
|
…..
|
I. a = 7, d = 3, n = 8, an = ?
In A.P. nth term is given by
an = a + (n − 1) d
= 7 + (8 − 1) 3
= 7 + (7) 3
= 7 + 21 = 28
Therefore , an = 28
II. Given
a = −18, n = 10, an = 0, d = ?
In A.P. nth term is given by
an = a + (n − 1) d
0 = − 18 + (10 − 1) d
18 = 9d
d = 18/9 = 2
Hence, common difference, d = 2
III. Given
d = −3, n = 18, an = −5
In A.P. nth term is given by
an = a + (n − 1) d
−5 = a + (18 − 1) (−3)
−5 = a + (17) (−3)
−5 = a − 51
a = 51 − 5 = 46
Hence, a = 46
IV. Given
a = −18.9, d = 2.5, an = 3.6, n = ?
In A.P. nth term is given by,
an = a + (n − 1) d
3.6 = − 18.9 + (n − 1) 2.5
3.6 + 18.9 = (n − 1) 2.5
22.5 = (n − 1) 2.5
(n ─ 1) = 22
(n ─ 1) = 9
Hence, n = 10
V. Given
a = 3.5, d = 0, n = 105, an =?
In A.P. nth term is given by
an = a + (n − 1) d
an = 3.5 + (105 − 1) 0
an = 3.5 + 104 × 0
an = 3.5
Hence, an = 3.5
Question 2:
Choose the correct choice in the following and justify
I. 30th term of the A.P: 10, 7, 4, …, is
A) 97 B) 77 C) – 77 D) − 87
II 11th term of the A.P
is
A) 28 B) 22 C) − 38 D) 
In A.P. nth term is given by
an = a + (n − 1) d
an = 10 + (30 − 1). ─3
an = 10 + 29 x ─3
an = 10 ─ 87
an = ─77
Hence, the answer is C.II) First term a = −3, Common difference, d = a2 − a1
In A.P. nth term is given by
an = a + (n − 1) d
Hence, the answer is B.
Next Page Ex - 5.2, Q. 3 and more