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| 1. |
Find the value of the middle term of the following A.P. -6 , -2 , 2 , . . . . . , 58 |
| Answer» According to question the given arithmetic progression: - 6, - 2, 2, ...,58.Here, a = -6, d\xa0= - 2 + 6 = 4 and an\xa0= 58 where a is first term and d is common difference{tex}\\Rightarrow{/tex}\xa0a + (n\xa0- 1)d = 58 {tex}\\Rightarrow{/tex}\xa0- 6 + (n - 1)4 = 58{tex}\\Rightarrow{/tex}\xa0(n - 1)4 = 64 {tex}\\Rightarrow{/tex}\xa0n\xa0- 1 = 16 {tex}\\Rightarrow{/tex}\xa0n\xa0= 17 (odd){tex}\\therefore{/tex}\xa0MIddle term =\xa0{tex}\\frac { 17 + 1 } { 2 } = \\frac { 18 } { 2 }{/tex} = 9th term{tex}\\therefore{/tex}\xa09th term is the middle term.Now, a9\xa0= a + 8d = -6 + 8\xa0{tex}\\times{/tex} 4 = -6 + 32 = 26 | |