The given sequence is AP or not ? If they are A.P. find the commo… - Vidyadip

Question

The given sequence is AP or not ? If they are A.P. find the common difference.
$0, – 4, – 8, – 12, . . .$

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Answer

$0, – 4, – 8, – 12, . . .$
Here, the first term, $a_1 = 0$
Second term, $a_2 = – 4$
$a_3 = – 8$
Now, common difference =$ a_2 – a_1 = – 4 – 0 = – 4$
Also, $a_3 – a_2 = – 8 – ( – 4) = – 8 + 4 = – 4$
Since, the common difference is same.
Hence the terms are in Arithmetic progression with common difference, $d = – 4.$

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