Saved Bookmarks
| 1. |
1+4+7+...X =207 find value of X |
| Answer» Given, a = 1, d = 4 -1 = 3.Let number of terms in the series be n.{tex}\\therefore \\quad S _ { n } = \\frac { n } { 2 } [ 2 a + ( n - 1 ) d ]{/tex}{tex}\\therefore \\quad \\frac { n } { 2 } [ 2 \\times 1 + ( n - 1 ) 3 ] = 287{/tex}or,\xa0{tex}\\frac { n } { 2 } [ 2 + ( 3 n - 3 ) ] = 287{/tex}or, {tex}n [3n - 1] = 574{/tex}or, {tex}3n^2- n - 574 = 0{/tex}{tex}3n^2 - n - 574 = 0{/tex}{tex}3n(n - 14) - 41(n - 14) = 0{/tex}{tex}(n - 14)(3n - 41) = 0{/tex}n - 14 = 0 or 3n - 41 = 0n = 14 or 3n = 41The 14th term is x.{tex}\\therefore{/tex}\xa0{tex}a + (n - 1)d = x{/tex}1 + 13\xa0{tex}\\times{/tex}\xa03 = x{tex}1 + 39 = x{/tex}x = 40 | |