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) a = 7, d = 3, n = 8, an = .....
(ii) a = -18, d = ...., n = 10, an = 0
(iii) a = ...., d = -3, n = 18, an = -5
(iv) a = -18.9, d = 2.5, n = ...., an = 3.6
(v) a = 3.5, d = 0, n = 105, an = ....
(i) Given,
First term, a = 7
Common difference, d = 3
Number of terms, n = 8,
We have to find the nth term, an = ?
As we know, for an A.P.,
an = a+(n−1)d
Putting the values,
= 7+(8 −1) 3
= 7+(7) 3
= 7+21 = 28
Hence, an = 28
(ii) Given,
First term, a = -18
Common difference, d = ?
Number of terms, n = 10
Nth term, an = 0
As we know, for an A.P.,
an = a+(n−1)d
Putting the values,
0 = − 18 +(10−1)d
18 = 9d
d = 18/9 = 2
Hence, common difference, d = 2
(iii) Given,
First term, a = ?
Common difference, d = -3
Number of terms, n = 18
Nth term, an = -5
As we know, for an A.P.,
an = a+(n−1)d
Putting the values,
−5 = a+(18−1) (−3)
−5 = a+(17) (−3)
−5 = a−51
a = 51−5 = 46
Hence, a = 46
(iv) Given,
First term, a = -18.9
Common difference, d = 2.5
Number of terms, n = ?
Nth term, an = 3.6
As we know, for an A.P.,
an = a +(n −1)d
Putting the values,
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
Hence, n = 10
(v) Given,
First term, a = 3.5
Common difference, d = 0
Number of terms, n = 105
Nth term, an = ?
As we know, for an A.P.,
an = a+(n −1)d
Putting the values,
an = 3.5+(105−1) 0
an = 3.5+104×0
an = 3.5
Hence, an = 3.5