Question

Fill in the blanks in the following table, given that a is the first term, d the common difference and a_n 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	…..

Answer 1

I. a = 7, d = 3, n = 8, a_n = ?

We know that,

For an A.P. a_n = a + (n − 1) d

= 7 + (8 − 1) 3

= 7 + (7) 3

= 7 + 21 = 28

Hence, a_n = 28

II. Given that

a = −18, n = 10, a_n = 0, d = ?

We know that,

a_n = a + (n − 1) d

0 = − 18 + (10 − 1) d

18 = 9d

Hence, common difference, d = 2

III. Given that

d = −3, n = 18, a_n = −5

We know that,

a_n = 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, a_n = 3.6, n = ?

We know that,

a_n = 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

Hence, n = 10

V. a = 3.5, d = 0, n = 105, a_n = ?

We know that,

a_n = a + (n − 1) d

a_n = 3.5 + (105 − 1) 0

a_n = 3.5 + 104 × 0

a_n = 3.5

Hence, a_n = 3.5