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Arithmetic Progressions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions3 Marks
Question
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
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Answer

Let A1, A2, A3, A4, A5 be five numbers between 8 and 26.
Let d be the common difference.
Then, we have:
 26 = A7
⇒ 26 = 8 + (7−1)d
⇒ 26 = 8 + 6d
⇒ d = 3
A1 = 8 + d = 8 + 3 = 11
A2 = 8 + 2d = 8 + 6 = 14
A3 = 8 + 3d = 8 + 9 = 17
A4 = 8 + 4d = 8 + 12 = 20
A5 = 8 + 5d = 8 + 15 = 23
Therefore, the five numbers are 11, 14, 17, 20, 23.

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