NCERT Class XI Mathematics - Sequences and Series - Solutions

Question : 28

Total: 106

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Solution:

Let A1,A2,A3,A4,A5 be numbers between 8 and 26 such that 8, A1,
A2,A3,A4,A5, 26 are in A.P., Here a = 8, l = 26, n = 7
∴ 26 = 8 + (7 – 1) d ⇒ 6d = 18 ⇒ d = 3
Thus A1 = a + d = 8 + 3 = 11; A2 = a + 2d = 8 + 6 = 14
A3 = a + 3d = 8 + 9 = 17; A4 = a + 4d = 8 + 12 = 20
A5 = a + 5d = 8 + 15 = 23
Hence five numbers between 8 and 26 are 11, 14, 17, 20, 23.

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