Question
Find the common difference and write the next four terms of the following arithmetic progressions:
$1, -2, -5, -8, .....$
$1, -2, -5, -8, .....$
✓
Answer
Here, $a_1 = 1, a_2 = -2, a_3 = -5, a_4 = -8, .....$
Now $a_2 - a_1 = -2 -1 = -3$
$a_3 - a_2 = -5 - (-2) = -5 + 2 = -3$
$a_4 - a_3 = -8 - (-5) = -8 + 5 = -3$
$\therefore$ It is an A.P. whose common difference is = -3
Now next four terms will be
$-8 - 3 = -11$
$-11 - 3 = -14$
$-14 - 3 = -17$
$-17 - 3 = -20$
$\therefore$ $-11, -14, -17, -20$ are four term next to these.
Now $a_2 - a_1 = -2 -1 = -3$
$a_3 - a_2 = -5 - (-2) = -5 + 2 = -3$
$a_4 - a_3 = -8 - (-5) = -8 + 5 = -3$
$\therefore$ It is an A.P. whose common difference is = -3
Now next four terms will be
$-8 - 3 = -11$
$-11 - 3 = -14$
$-14 - 3 = -17$
$-17 - 3 = -20$
$\therefore$ $-11, -14, -17, -20$ are four term next to these.
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