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Please solve this problem sir
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Asked by sanjaysingh.srct | 27 Jul, 2019, 22:29: PM
answered-by-expert Expert Answer
Let the first term of an A.P. and G.P be 'a' since they are equal
Common difference 'd' and common ratio 'r'
Therefore, a+d=ar  i.e. d=a(r-1)
T h i r d space t e r m space o f space A. P. space a subscript 3 equals a plus 2 d equals a subscript 2 plus d equals a r plus d equals a r plus a left parenthesis r minus 1 right parenthesis equals a left parenthesis 2 r minus 1 right parenthesis T h i r d space t e r m space o f space G. P space t subscript 3 equals a r squared S i m i l a r l y comma space space a subscript 4 equals a left parenthesis 3 r minus 2 right parenthesis comma space t subscript 4 equals a r cubed space a subscript 5 equals a left parenthesis 4 r minus 3 right parenthesis comma space t subscript 5 equals a r to the power of 4 space space a n d space s o space o n... C l e a r l y comma space 2 r minus 1 less than r squared 3 r minus 2 less than r cubed 4 r minus 3 less than r to the power of 4 space a n d space s o space o n... T h e r e f o r e comma space space a open parentheses 2 r minus 1 close parentheses less than a r squared a open parentheses 3 r minus 2 close parentheses less than a r cubed a open parentheses 4 r minus 3 close parentheses less than a r to the power of 4 space a n d space s o space o n... H e n c e comma space a subscript 3 less than t subscript 3 comma space a subscript 4 less than t subscript 4 space a n d space s o space o n... H e n c e comma space o t h e r space t e r m s space o f space A. P. space d o e s space n o t space e x c e e d space t h e space c o r r e s p o n d i n g space t e r m space o f space t h e space G. P.
Answered by Renu Varma | 29 Jul, 2019, 10:35: AM

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