If 7 times the 7th term of an AP is equal to 11 times the 11th term,show that the 18th term of the AP is 0.

Asked by derrindarren | 30th Dec, 2015, 08:35: PM

Expert Answer:

L e t space apostrophe a apostrophe space b e space t h e space i n i t i a l space t e r m space a n d space apostrophe d apostrophe space b e space t h e space c o m m o n space d i f f e r e n c e space o f space t h e space A P. 7 t h space t e r m space o f space t h e space A P space i s space a subscript 7 space a n d space 11 t h space t e r m space o f space t h e space A P space i s space a subscript 11 a subscript 7 equals a plus open parentheses 7 minus 1 close parentheses d... left parenthesis 1 right parenthesis a n d a subscript 11 equals a plus open parentheses 11 minus 1 close parentheses d... left parenthesis 2 right parenthesis G i v e n space t h a t space 7 t i m e s space 7 t h space t e r m space i s space e q u a l space t o space 11 space t i m e s space 11 t h space t e r m. T h u s space f r o m space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma 7 open square brackets a plus open parentheses 7 minus 1 close parentheses d close square brackets equals 11 open square brackets a plus open parentheses 11 minus 1 close parentheses d close square brackets rightwards double arrow 7 open square brackets a plus 6 d close square brackets equals 11 open square brackets a plus 10 d close square brackets rightwards double arrow 7 a plus 42 d equals 11 a plus 110 d rightwards double arrow 11 a plus 110 d minus 7 a minus 42 d equals 0 rightwards double arrow 4 a plus 68 d equals 0 rightwards double arrow 4 open square brackets a plus 17 d close square brackets equals 0 rightwards double arrow 4 open square brackets a plus open parentheses 18 minus 1 close parentheses d close square brackets equals 0 rightwards double arrow 4 a subscript 18 equals 0 comma space w h e r e space a subscript 18 equals a plus open parentheses 18 minus 1 close parentheses d rightwards double arrow a subscript 18 equals 0

Answered by Vimala Ramamurthy | 31st Dec, 2015, 09:13: AM