Is this –10, –6, –2, 2, .... an AP? If it forms an AP, find the c… - Vidyadip

Question

Is this $–10, –6, –2, 2, ....$ an $AP$? If it forms an $AP$, find the common difference d and write three more terms.

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Answer

$-10, -6, -2, 2, ....$
$a_2 - a_1 = -6 - (-10) = -6 + 10 = 4$
$a_3 - a_2 = -2 - (-6) = -2 + 6 = 4$
$a_4 - a_3 = 2 - (-2) = 2 + 2 = 4$
i.e. $a_{k+1} - a_k$_ is the same every time.
So, the given lists of numbers form an AP with the common difference $d = 4.$
The next three terms are:
$2 + 4 = 6, 6 + 4 = 10$ and $10 + 4 = 14$

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