If the 5th term of an AP is 0,show that its 33rd term is 4 times its 12th term.

Asked by derrindarren | 30th Dec, 2015, 08:38: 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 g i v e n space A P 5 t h space t e r m space o f space t h e space A P space i s space a subscript 5 comma space 33 r d space t e r m space o f space t h e space A P space i s space a subscript 33 space a n d space 12 t h space t e r m space i s space a subscript 12 rightwards double arrow a subscript 5 equals a plus open parentheses 5 minus 1 close parentheses d semicolon space a subscript 33 equals a plus open parentheses 33 minus 1 close parentheses d space a n d space a subscript 12 equals a plus open parentheses 12 minus 1 close parentheses d rightwards double arrow a subscript 5 equals a plus 4 d semicolon space a subscript 33 equals a plus 32 d space a n d space space a subscript 12 equals a plus 11 d G i v e n space t h a t space 5 t h space t e r m space i s space 0 rightwards double arrow a plus 4 d equals 0... left parenthesis 1 right parenthesis rightwards double arrow a equals negative 4 d... left parenthesis 2 right parenthesis M u l t i p l y i n g space e q u a t i o n space left parenthesis 1 right parenthesis space b y space 2 space w e space h a v e comma 2 a plus 8 d equals 0... left parenthesis 3 right parenthesis  C o n s i d e r space a subscript 33 colon a subscript 33 equals a plus 32 d space space space space space space equals a plus 36 d minus 4 d space space space open square brackets r e w r i t i n g space 32 d space a s space 36 d minus 4 d close square brackets space space space space space space equals a plus 36 d plus a space space space space space space open square brackets f r o m space e q u a t i o n space left parenthesis 2 right parenthesis close square brackets space space space space space space equals 2 a plus 36 d space space space space space space equals 2 a plus 36 d plus 0 space space space space open square brackets a d d i n g space 0 space w i l l space n o t space c h a n g e space t h e space v a l u e space o f space t h e space e x p r e s s i o n close square brackets space space space space space space equals 2 a plus 36 d plus 2 a plus 8 d space space space space space space equals 4 a plus 44 d space space space space space space equals 4 open parentheses a plus 11 d close parentheses space space space space space space equals 4 open parentheses a plus open parentheses 12 minus 1 close parentheses d close parentheses space space space space space space equals 4 a subscript 12

Answered by Vimala Ramamurthy | 31st Dec, 2015, 10:23: AM