Question

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 AP:
| a| d| n| $a_n$
---|---|---|---|---
(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 + 2
= 28
Hence, $a_n$= 28

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(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
d = $\frac{18}{9}$= 2
Hence, common difference, d = 2

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(iii) Given that d = −3, n = 18, an = −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

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(iv) a = −18.9, d = 2.5, an = 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
(n-1) = $\frac{22.5}{2.5}$
n-1 = 9
n = 10
Hence, n = 10

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(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