Which of the following list of numbers form A.R's? If they form an A.P., find the common difference d and also write its next three terms.
- 1.2, - 3.2, - 5.2, - 7.2, ...
We have,
a2 – a1 = -3.2 – (-1.2) =-3.2 + 1.2 = -2.0
a3 – a2 = -5.2 – (-3.2) = -5.2 + 3.2 = -2.0
a4 – a3 = -7.2 – (-5.2) = -7.2 + 5.2 = -2.0
i.e. ak+1 – ak is the same every time.
So, the given list of numbers forms an AP with the common difference d = -2
Now, we have to find the next three terms.
We have a1 = -1.2, a2 = -3.2, a3 = -5.2 and a4 = -7.2
Now, we will find a5, a6 and a7
So, a5 = -7.2 + (-2) = -7.2 – 2.0 = -9.2
a6 = -9.2 + (-2) = -9.2 – 2.0 = -11.2
and a7 = -11.2 + (-2) = -11.2 – 2.0 = -13.2
Hence, the next three terms are -9.2, -11.2 and -13.2
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