Question
Is this $–1.2, –3.2, –5.2, –7.2, …$. an AP? If it forms an $AP$, find the common difference d and write three more terms.
✓
Answer
$-1.2, -3.2, -5.2, -7.2, ....$
$a^2 - a^1 = -3.2 - (-1.2) = -3.2 + 1.2 = -2.0$
$a^3 - a^2 = -5.2 - (-3.2) = -5.2 + 3.2 = -2.0$
$a^4 - a^3 = -7.2 - (-5.2) = -7.2 + 5.2 = -2.0$
i.e. $a_{k+1} - a_k$_ is the same everytime,
So, the given list of numbers form an AP with the common differenced $d = -2.0$
The next three terms are:
$-7.2 + (-2.0) = -9.2$
$-9.2 + (-2.0) = -11.2$
and$ -11.2 + (-2.0) = -13.2$
$a^2 - a^1 = -3.2 - (-1.2) = -3.2 + 1.2 = -2.0$
$a^3 - a^2 = -5.2 - (-3.2) = -5.2 + 3.2 = -2.0$
$a^4 - a^3 = -7.2 - (-5.2) = -7.2 + 5.2 = -2.0$
i.e. $a_{k+1} - a_k$_ is the same everytime,
So, the given list of numbers form an AP with the common differenced $d = -2.0$
The next three terms are:
$-7.2 + (-2.0) = -9.2$
$-9.2 + (-2.0) = -11.2$
and$ -11.2 + (-2.0) = -13.2$
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