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if the sum of n term of an A.P is 3(n)2 +5n, then which of its terms is 164 |
| Answer» Given:Sn = 3n2 + 5n\xa0and am = 164Put n = 1 and n = 2 in Sn we get, S1 = 3 + 5 = 8\xa0{tex}\\Rightarrow {/tex}\xa0a = 8 ..........(i)and S2 = 3(4) + 5(2) = 12 + 10 = 22We have an = Sn - Sn-1{tex}\\therefore{/tex}\xa0a2 = S2 - S1{tex}\\Rightarrow{/tex}\xa0a2 = 22 - 8 = 14Now\xa0d = a2\xa0- a1\xa0= 14 - 8 = 6{tex}\\therefore{/tex}\xa0am = 164\xa0{tex}\\Rightarrow {/tex}\xa0a + (m - 1)d = 164\xa0{tex}\\Rightarrow {/tex}\xa08 + (m - 1)6 = 164{tex}\\Rightarrow {/tex}\xa08 + 6m - 6 = 164{tex}\\Rightarrow {/tex}\xa06m = 162{tex}\\Rightarrow m = {{162} \\over 6} = 27{/tex} | |