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Question
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Solution
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 = a7
\[\Rightarrow\] 26 = 8 + \[\left( 7 - 1 \right)\] d
\[\Rightarrow\] d = 3
\[\Rightarrow\] 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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