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.
i. a = 7, d = 3 and n = 8 an = ?
ii. a = - 18, n = 10, an = 0, d = ?
iii. d = -3, n = 18, an = -5, a = ?
iv. a = -18.9, d = 2.5, an = 3.6, n = ?
v. a = 3.5, d = 0, n = 105, an = ?
Explanatory Answer
i. a = 7, d = 3 and n = 8 an = ?
an = a + (n – 1)d
∴ a8 = 7 + (8 – 1) × 3
= 7 + (7 × 3)
= 28
ii. a = - 18, n = 10, an = 0, d = ?
an = a + (n – 1) d
0 = -18 + (10 – 1) d
9d = 18
d = \\frac{18}{9}) = 2
iii. d = -3, n = 18, an = -5, a = ?
an = a + (n – 1)d
-5 = a + (18 – 1) × (-3)
-5 = a - 51
∴ a = 51 – 5 = 46
iv. a = -18.9, d = 2.5, an = 3.6, n = ?
an = a + (n – 1) d
3.6 = -18.9 + (n – 1)(2.5)
22.5 = (n – 1)(2.5)
(n – 1) = \\frac{22.5}{2.5}) = 9
Or n = 10
v. a = 3.5, d = 0, n = 105, an = ?
an = a + (n – 1) d
an = 3.5 + (105 - 1) × 0
a105 = 3.5
If d = 0, all terms of the arithmetic progression are the same.