Q. 6 F5.0( 1 Vote )

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.

0, - 4, - 8, - 12,

Answer :

We have,


a2 – a1 = -4 – 0 = -4


a3 – a2 =-8 – (-4) = -8 + 4 = -4


a4 – a3 =-12 – (-8) = -12 + 8= -4


i.e. ak+1 – ak is the same every time.


So, the given list of numbers forms an AP with the common difference d = -4


Now, we have to find the next three terms.


We have a1 = 0, a2 = -4, a3 = -8 and a4 = -12


Now, we will find a5, a6 and a7


So, a5 = -12 + (-4) = -12 – 4 = -16


a6 = -16 + (-4) = -16 – 4 = -20


and a7 = -20 + (-4) = -20 – 4 = -24


Hence, the next three terms are -16, -20 and -24


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