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| 1. |
Insert five number between 8 and 26 such that the resulting sequence is an A.P. |
| Answer» Let A1, A2, A3, A4, and A5\xa0be five numbers between 8 and 26 such that8, A1, A2, A3, A4, A5, 26 is an A.P.Here,\xa0a\xa0= 8,\xa0b\xa0= 26,\xa0n\xa0= 7Therefore, 26 = 8 + (7 – 1)\xa0d⇒ 6d\xa0= 26 – 8 = 18⇒\xa0d\xa0= 3A1\xa0=\xa0a\xa0+\xa0d\xa0= 8 + 3 = 11A2\xa0=\xa0a\xa0+ 2d\xa0= 8 + 2 × 3 = 8 + 6 = 14A3\xa0=\xa0a\xa0+ 3d\xa0= 8 + 3 × 3 = 8 + 9 = 17A4\xa0=\xa0a\xa0+ 4d\xa0= 8 + 4 × 3 = 8 + 12 = 20A5\xa0=\xa0a\xa0+ 5d\xa0= 8 + 5 × 3 = 8 + 15 = 23Thus, the required five numbers between 8 and 26 are 11, 14, 17, 20, and 23. | |