Write the sequence with nth term:
(i)
(ii)
(iii)
(iv)
Show that all of the above sequences form A.P.
(i) Put n = 1
A1= 3 + 4(1) = 7
Put n = 2
A2= 3 + 4(2) = 11
Put n = 3
A3= 3 + 4(3) = 15
Common difference, d1= a2 – a1 = 11 – 7 = 4
Common difference, d2= a3 – a2 = 15 – 11 = 4
Since, d1 = d2
Therefore, it’s an A.P. with sequence 7, 11, 15,…
(ii) Put n = 1
A1= 5 + 2(1) = 7
Put n = 2
A2= 5 + 2(2) = 9
Put n = 3
A3= 5 + 2(3) = 11
Common difference, d1= a2 – a1= 9 – 7 = 2
Common difference, d2= a3 – a2= 11 – 9 = 2
Since, d1 = d2
Therefore, it’s an A.P. with sequence 7, 9, 11,…
(iii) Put n = 1
A1= 6 – 1 = 5
Put n = 2
A2= 6 – 2 = 4
Put n = 3
A3= 6 – 3 = 3
Common difference, d1= a2 – a1= 4 – 5 = -1
Common difference, d2 = a3- a2= 3 – 4 = -1
Since, d1=d2
Therefore, it’s an A.P. with sequence 5, 4 , 3,…
(iv) Put n = 1
A1= 9 – 5(1) = 4
Put n = 2
A2= 9 – 5(2) = -1
Put n = 3
A3= 9 – 5(3) = -6
Common difference, d1= a2 – a1 = -1 – 4 = -5
Common difference,d2= a3 – a2 = -6 – (-1) = -5
Since, d1=d2
Therefore, it’s an A.P. with sequence 4, -1, -6,…