Question
Insert five numbers between $8$ and $26$ such that the resulting sequence is an A.P.
✓
Answer
Let $A_1, A_2, A_3, A_4, A_5 $ be five numbers between $8$ and $26.$
Let d be the common difference.
Then, we have:
$26 = A_7$
$\Rightarrow 26 = 8 + (7−1)d$
$\Rightarrow 26 = 8 + 6d$
$\Rightarrow d = 3$
$A_1 = 8 + d = 8 + 3 = 11$
$A_2 = 8 + 2d = 8 + 6 = 14$
$A_3 = 8 + 3d = 8 + 9 = 17$
$A_4 = 8 + 4d = 8 + 12 = 20$
$A_5 = 8 + 5d = 8 + 15 = 23$
Therefore, the five numbers are $11, 14, 17, 20, 23.$
Let d be the common difference.
Then, we have:
$26 = A_7$
$\Rightarrow 26 = 8 + (7−1)d$
$\Rightarrow 26 = 8 + 6d$
$\Rightarrow d = 3$
$A_1 = 8 + d = 8 + 3 = 11$
$A_2 = 8 + 2d = 8 + 6 = 14$
$A_3 = 8 + 3d = 8 + 9 = 17$
$A_4 = 8 + 4d = 8 + 12 = 20$
$A_5 = 8 + 5d = 8 + 15 = 23$
Therefore, the five numbers are $11, 14, 17, 20, 23.$
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