Question

Question 1 Fill in the blanks in the following table, given that a is the first term, d the common difference and an the n th 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 …..

Class 10 - Math - Arithmetic Progressions Page 105

Answer 1

In an AP, (a) is the first term , d is the common difference & n is the number of terms & an is the nth term.
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Solution:

(i)
Given:
a = 7, d = 3, n = 8, an = ?

We know that,
an = a + (n − 1) d

= 7 + (8 − 1) 3
= 7 + (7) 3
= 7 + 21 = 28

Hence, an = 28

(ii) Given:

a = −18, n = 10, an = 0, d = ?

We know that,
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

We know that,
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 = ?

We know that,
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) = 22.5/2.5
n – 1 = 9
n = 10

Hence, n = 10

(v) Given :
a = 3.5, d = 0, n = 105, an = ?

We know that,
an = a + (n − 1) d

an = 3.5 + (105 − 1) 0
an = 3.5 + 104 × 0
an = 3.5

Hence, an = 3.5

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Hope this will help you.....

Answer 2

(i) a = 7, d = 3, n = 8, an = ?
We know that,
For an A.P. an = a + (n − 1) d
= 7 + (8 − 1) 3
= 7 + (7) 3
= 7 + 21 = 28
Hence, an = 28

(ii) Given that
a = −18, n = 10, an = 0, d = ?
We know that,
an = a + (n − 1) d
0 = − 18 + (10 − 1) d
18 = 9d
d = 18/9 = 2
Hence, common difference, d = 2

(iii) Given that
d = −3, n = 18, an = −5
We know that,
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) a = −18.9, d = 2.5, an = 3.6, n = ?
We know that,
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) = 22.5/2.5
n - 1 = 9
n = 10
Hence, n = 10

(v) a = 3.5, d = 0, n = 105, an = ?
We know that,
an = a + (n − 1) d
an = 3.5 + (105 − 1) 0
an = 3.5 + 104 × 0
an = 3.5
Hence, an = 3.5