Q)

Asked by araima2001 | 22nd Mar, 2017, 01:37: PM

Expert Answer:

begin mathsize 16px style Consider comma space
straight b subscript straight n equals log subscript 5 open parentheses straight a subscript straight n close parentheses
space space space space equals log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses to the power of straight n close square brackets
space space space space space equals straight n log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets
Then
straight b subscript 1 equals log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets space space space space space space space space space space space..... open parentheses straight i close parentheses
straight b subscript 2 equals 2 log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets space space space space space space space space space..... open parentheses ii close parentheses
straight b subscript 3 equals 3 log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets space space space space space space space space space space..... open parentheses iii close parentheses
From space open parentheses straight i close parentheses comma open parentheses ii close parentheses comma open parentheses iii close parentheses
straight b subscript 2 minus straight b subscript 1 equals 2 log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets space minus log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets
space space space space space space space space space space space space space equals log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space........ open parentheses iv close parentheses
straight b subscript 3 minus straight b subscript 2 equals 3 log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets space minus 2 log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets
space space space space space space space space space space space space space equals log subscript 5 open square brackets log open parentheses 7 over 5 close parentheses close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space........ open parentheses straight v close parentheses
Hence comma space from space open parentheses iv close parentheses space and space open parentheses straight v close parentheses
we space can space say space that space straight b subscript straight n space is space in space Arithmetic space Progression.

space space space end style

Answered by Sneha shidid | 22nd Mar, 2017, 04:22: PM