Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(i) -1.2, -3.2, -5.2, -7.2 …
(ii) -10, – 6, – 2, 2 …
(i) Given, -1.2, – 3.2, -5.2, -7.2 …
a2 – a1 = (-3.2)-(-1.2) = -2
a3 – a2 = (-5.2)-(-3.2) = -2
a4 – a3 = (-7.2)-(-5.2) = -2
Since, an+1 – an or common difference is same every time.
Therefore, d = -2 and the given series are in A.P.
Hence, next three terms are;
a5 = – 7.2-2 = -9.2
a6 = – 9.2-2 = – 11.2
a7 = – 11.2-2 = – 13.2
(ii) Given, -10, – 6, – 2, 2 …
Here, the terms and their difference are;
a2 – a1 = (-6)-(-10) = 4
a3 – a2 = (-2)-(-6) = 4
a4 – a3 = (2 -(-2) = 4
Since, an+1 – an or the common difference is same every time.
Therefore, d = 4 and the given numbers are in A.P.
Hence, next three terms are;
a5 = 2+4 = 6
a6 = 6+4 = 10
a7 = 10+4 = 14