(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