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CBSE Class 10 Answered

The sum of n terms of two A.P's are in the ratio 5n+9:9n+6. Then, the ratio of their 18th term is:   179/321 178/321 175/321 176/321 sir,please explain me clearly and in easy steps.  
Asked by Shambhu Nath Pandey | 04 Feb, 2016, 12:26: PM
answered-by-expert Expert Answer

mibegin mathsize 14px style L e t space a subscript 1 space a n d space a subscript 2 space b e space t h e space f i r s t space t e r m s space o f space t h e space t w o space g i v e n space A. P. space a n d space d subscript 1 space a n d space d subscript 2 space b e space t h e i r space r e s p e c t i v e space c o m m o n space d i f f e r e n c e s comma T h e n comma fraction numerator begin display style n over 2 end style left square bracket 2 a subscript 1 plus left parenthesis n minus 1 right parenthesis d subscript 1 right square bracket over denominator n over 2 left square bracket 2 a subscript 2 plus left parenthesis n minus 1 right parenthesis d subscript 2 right square bracket end fraction equals fraction numerator 5 n plus 4 over denominator 9 n plus 6 end fraction rightwards double arrow fraction numerator a subscript 1 plus begin display style fraction numerator n minus 1 over denominator 2 end fraction end style d subscript 1 over denominator a subscript 2 plus fraction numerator n minus 1 over denominator 2 end fraction d subscript 2 end fraction equals fraction numerator 5 n plus 4 over denominator 9 n plus 6 end fraction r a t i o space o f space t h e space 18 t h space t e r m s equals fraction numerator a subscript 1 plus 17 d subscript 1 over denominator a subscript 2 plus 17 d subscript 2 end fraction T o space o b t a i n space t h e space r e q u i r e d space r a t i o comma space p u t space fraction numerator n minus 1 over denominator 2 end fraction equals 17 space i. e. comma space n equals 35 rightwards double arrow R e q u i r e d space r a t i o equals fraction numerator 5 cross times 35 plus 4 over denominator 5 cross times 35 plus 6 end fraction equals 179 over 321 end style

Answered by | 04 Feb, 2016, 06:01: PM

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