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Question
Check if given series is AP or not? If they form an AP, find the common difference d and write three more terms.
0,−4,−8,−12,....
0,−4,−8,−12,....
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Solution
The given series is 0,−4,−8,−12,⋯.
a2−a1=−4−0
=−4
a3−a2=−8−(−4)
=−4
a4−a3=−12−(−8)
=−4
This shows
that the difference is same, so the given series is in A.P. with common
difference −4. The next three
terms are,
a5=−12+(−4)
=−16
a6=−16+(−4)
=−20
a7=−20+(−4)
=−24
The given series is 0,−4,−8,−12,⋯.
a2−a1=−4−0
=−4
a3−a2=−8−(−4)
=−4
a4−a3=−12−(−8)
=−4
This shows that the difference is same, so the given series is in A.P. with common difference −4. The next three terms are,
a5=−12+(−4)
=−16
a6=−16+(−4)
=−20
a7=−20+(−4)
=−24
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