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| 1. |
Prove that am + n + am - n =2am |
| Answer» Let the first term and common difference of the A. P. be\xa0a\xa0and\xa0d\xa0respectively.Then (m\xa0+\xa0n)th\xa0term (am\xa0+\xa0n\xa0) =\xa0a\xa0+ (m\xa0+\xa0n\xa0– 1)\xa0dand (m\xa0–\xa0n)th\xa0term (am –\xa0n\xa0) =\xa0a\xa0+ (m\xa0–\xa0n\xa0– 1)\xa0d\xa0am +\xa0n\xa0+\xa0am –\xa0n\xa0=\xa0a\xa0+ (m\xa0+\xa0n\xa0– 1)\xa0d\xa0+\xa0a\xa0+ (m\xa0–\xa0n\xa0– 1)\xa0d= 2a\xa0+ (m\xa0+\xa0n\xa0– 1\xa0+\xa0m\xa0–\xa0n\xa0– 1)\xa0d= 2a\xa0+ (2m\xa0– 2)\xa0d\xa0= 2a\xa0+ 2 (m\xa0– 1)\xa0d= 2[a\xa0+ (m\xa0– 1)\xa0d] = 2am\xa0= 2 (m\xa0th\xa0term) | |