The pth term of an AP is 20 and its qth term is 10 . show that the sum 
of its (p+q)  terms is p+q/2 {30+10/p-q}
 

Asked by AAkshaya | 11th Jul, 2017, 08:43: PM

Expert Answer:

begin mathsize 16px style From space the space given space information
straight a plus open parentheses straight p minus 1 close parentheses straight d equals 20.............. left parenthesis straight i right parenthesis
straight a plus open parentheses straight q minus 1 close parentheses straight d equals 10.............. left parenthesis ii right parenthesis
Solving space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
you space will space get space straight d equals fraction numerator 10 over denominator straight p minus straight q end fraction comma space straight a equals fraction numerator 10 straight p minus 20 straight q plus 10 over denominator straight p minus straight q end fraction
straight S subscript straight p plus straight q end subscript equals open parentheses fraction numerator straight p plus straight q over denominator 2 end fraction close parentheses open square brackets 2 cross times fraction numerator 10 straight p minus 20 straight q plus 10 over denominator straight p minus straight q end fraction plus open parentheses straight p plus straight q minus 1 close parentheses cross times fraction numerator 10 over denominator straight p minus straight q end fraction close square brackets

straight S subscript straight p plus straight q end subscript equals open parentheses fraction numerator straight p plus straight q over denominator 2 end fraction close parentheses open square brackets fraction numerator 20 straight p minus 40 straight q plus 10 plus 10 straight p plus 10 straight q minus 10 over denominator straight p minus straight q end fraction close square brackets
straight S subscript straight p plus straight q end subscript equals open parentheses fraction numerator straight p plus straight q over denominator 2 end fraction close parentheses open square brackets fraction numerator 30 straight p minus 30 straight q plus 10 over denominator straight p minus straight q end fraction close square brackets
straight S subscript straight p plus straight q end subscript equals open parentheses fraction numerator straight p plus straight q over denominator 2 end fraction close parentheses open square brackets fraction numerator 30 open parentheses straight p minus straight q close parentheses over denominator straight p minus straight q end fraction plus fraction numerator 10 over denominator straight p minus straight q end fraction close square brackets
straight S subscript straight p plus straight q end subscript equals open parentheses fraction numerator straight p plus straight q over denominator 2 end fraction close parentheses open square brackets 30 plus fraction numerator 10 over denominator straight p minus straight q end fraction close square brackets end style

Answered by Sneha shidid | 12th Jul, 2017, 09:32: AM