Fill in the blanks in the following table, given that a is the first term, d the commondifference and the nth term of the AP

(i) Given: a = 7, d = 3 and n = 8,

a_n = ?

We know:

a_n = a + (n – 1)d

Thus, a_n = 7 + (8 – 1)3 = 7 + 21 = 28

(ii) Given a = - 18, n = 10, a_n = 0, d = ?

We know that a_n = a + (n – 1)d

Thus, 0 = - 18 + (10 – 1)d

 0 = - 18 + 9d

Or, 9d = 18

Or, d = 18/9 = 2

(iii) Given d = - 3, n = 18, a_n = - 5, a = ?

We know that, a_n = a + (n – 1)d

Or, - 5 = a + (18 – 1) (- 3)

Or, - 5 = a – 51

Or, a = - 5 + 51 = 46

(iv) Given a = - 18.9, d = 2.5, a_n = 3.6, n = ?

We know that, a_n = a + (n – 1)d

Or, 3.6 = – 18.9 + (n – 1)2.5

Or, 2.5(n – 1) = 3.6 + 18.9 = 22.5

n – 1 = 22.5/2.5 = 9

n = 9 + 1 = 10

(v) Given that a = 3.5, d = 0, n = 105, a_n= ?

We know:,

a_n = a + (n – 1)d

a_n = 3.5 + (104 – 1)0

a_n = 3.5 + 0

          = 3.5