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.
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.

(i) Given here,

The first term, a = ?

The common difference, d = -3

Number of terms given, n = 18

Nth term, an = -5

As we all know, for an A.P.,

an = a+(n−1)d

Putting the values together,

−5 = a+(18−1) (−3)

−5 = a+(17) (−3)

−5 = a−51

a = 51−5 = 46

Therefore, a = 46

(ii) Given here,

The first term, a = -18.9

The common difference, d = 2.5

Number of terms given, n = ?

Nth term, an = 3.6

As we all know, for an A.P.,

an = a +(n −1)d

Putting the values together,

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

Therefore, n = 10