16 2nd part

Asked by lovemaan5500 | 17th Jul, 2018, 06:36: PM

Expert Answer:

begin mathsize 16px style straight S subscript straight n equals straight n over 2 open square brackets 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d close square brackets
6 equals 3 over 2 open parentheses 2 straight a plus 2 straight d close parentheses
6 equals 3 straight a plus 3 straight d..... left parenthesis straight i right parenthesis
straight S subscript 6 equals 6 over 2 open parentheses 2 straight a plus 5 straight d close parentheses
3 equals 6 straight a plus 15 straight d........ left parenthesis ii right parenthesis
Solving space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
we space get space straight a space equals space 3 space and space straight d equals negative 1
2 open parentheses 2 straight n plus 1 close parentheses straight S subscript straight n plus 4 end subscript
equals 2 open parentheses 2 straight n plus 1 close parentheses fraction numerator straight n plus 4 over denominator 2 open square brackets 2 straight a plus open parentheses straight n plus 3 right parenthesis straight d close parentheses close square brackets end fraction
equals left parenthesis 2 straight n plus 1 right parenthesis left parenthesis straight n plus 4 right parenthesis left parenthesis 3 minus straight n right parenthesis
Solving space RHS space we space get space
left parenthesis straight n plus 4 right parenthesis straight S subscript 2 straight n plus 1 end subscript equals left parenthesis 2 straight n plus 1 right parenthesis left parenthesis straight n plus 4 right parenthesis left parenthesis 3 minus straight n right parenthesis
Hence comma
2 open parentheses 2 straight n plus 1 close parentheses straight S subscript straight n plus 4 end subscript equals left parenthesis straight n plus 4 right parenthesis straight S subscript 2 straight n plus 1 end subscript


end style

Answered by Sneha shidid | 19th Jul, 2018, 10:06: AM