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) Given a = 7, d = 3, n = 8. Find \(a_n\).
The formula for the nth term of an A.P. is \(a_n\) = a + (n − 1) d.
Substituting the values: \(a_n\) = 7 + (8 − 1) × 3 = 7 + (7) × 3 = 7 + 21 = 28.
Therefore, \(a_n\) = 28.

---

(ii) Given a = −18, n = 10, \(a_n\) = 0. Find d.
Using the formula \(a_n\) = a + (n − 1) d.
0 = −18 + (10 − 1) d
18 = 9d
d = \(\frac{18}{9}\) = 2.
Hence, the common difference, d = 2.

---

(iii) Given d = −3, n = 18, \(a_n\) = −5. Find a.
Using the formula \(a_n\) = a + (n − 1) d.
−5 = a + (18 − 1) (−3)
−5 = a + (17) (−3)
−5 = a − 51
a = 51 − 5 = 46.
Hence, a = 46.

---

(iv) Given a = −18.9, d = 2.5, \(a_n\) = 3.6. Find n.
Using the formula \(a_n\) = 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.

---

(v) Given a = 3.5, d = 0, n = 105. Find \(a_n\).
Using the formula \(a_n\) = 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.