The ratio between the sum of two Ap is (3 n +8): (7 n +15) find the ratio of 12 the term

The ratio between the sum of two Ap is (3 n +8): (7 n +15) find the ra

1.	The ratio between the sum of two Ap is (3 n +8): (7 n +15) find the ratio of 12 the term
Answer» Let a1, a2 and d1, d2 are the first term and common difference of two A. P. S respectively.A T Q {tex}\\frac{{\\frac{n}{2}}}{{\\frac{n}{2}}}\\frac{{\\left[ {2{a_1} + \\left( {n - 1} \\right){d_1}} \\right]}}{{\\left[ {2{a_2} + \\left( {n - 1} \\right){d_2}} \\right]}} = \\frac{{3n + 8}}{{7n + 15}}{/tex}{tex}\\frac { 12 \\text { th term of Ist } \\mathrm { A } . \\mathrm { P } } { 12 \\mathrm { th } \\text { term of } 2 \\mathrm { ndA.P } } = \\frac { a _ { 1 } + 11 d _ { 1 } } { a _ { 2 } + 11 d _ { 2 } }{/tex}put n = 23 in eq (i){tex}\\frac { 2 a _ { 1 } + 22 d _ { 1 } } { 2 a _ { 2 } + 22 d _ { 2 } } = \\frac { 3 \\times 23 + 8 } { 7 \\times 23 + 15 }{/tex}{tex}\\frac { a _ { 1 } + 11 d _ { 1 } } { a _ { 2 } + 11 d _ { 2 } } = \\frac { 7 } { 16 }{/tex}