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 = ?
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
