In the table below, some arithmetic sequences are given with two numbers against each. Check whether each belongs to the sequence or not.
a) a = 11
d = 22-11 = 11
i) let an = 123
an = a + (n-1)×d
∴ n = 11.18
Since, n is not an integer, 123 is not a part of sequence
ii) let an = 132
an = a + (n-1)×d
∴ n = 12
Since, n is an integer, 132 is a part of sequence
b) a = 12
d = 23-12 = 11
i) let an = 100
an = a + (n-1)×d
∴ n = 9
Since, n is an integer, 100 is a part of sequence
ii) let an = 1000
an = a + (n-1)×d
∴ n = 90.81
Since, n is not an integer, 1000 is not a part of sequence
c) a = 21
d = 32-21 = 11
i) let an = 100
an = a + (n-1)×d
∴ n = 8.18
Since, n is not an integer, 100 is not a part of sequence
ii) let an = 1000
an = a + (n-1)×d
∴ n = 90
Since, n is an integer, 1000 is a part of sequence
d) a = 1/4
d = (1/2)-(1/4) = 1/4
i) let an = 3
an = a + (n-1)×d
∴ n = 12
Since, n is an integer, 3 is a part of sequence
ii) let an = 4
an = a + (n-1)×d
∴ n = 16
Since, n is an integer, 4 is a part of sequence
e) a = 3/4
d = (3/2)-(3/4) = 3/4
i) let an = 3
an = a + (n-1)×d
∴ n = 4
Since, n is an integer, 3 is a part of sequence
ii) let an = 4
an = a + (n-1)×d
∴ n = 5.33
Since, n is not an integer, 4 is not a part of sequence