23rd sum

 

Asked by lovemaan5500 | 28th Jan, 2019, 06:33: AM

Expert Answer:

Let the first term of the first AP be a and common difference be d and the first term of a second AP be A and common diffrence be D.
6th term of the first A.P.
t6 = a + 5d and
6th term of the second A.P.
t6 = A + 5D
According to the question,
begin mathsize 16px style fraction numerator begin display style straight n over 2 open square brackets 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d close square brackets end style over denominator straight n over 2 open square brackets 2 straight A plus left parenthesis straight n minus 1 right parenthesis straight D close square brackets end fraction equals fraction numerator 7 straight n minus 5 over denominator 5 straight n plus 17 end fraction
fraction numerator begin display style open square brackets straight a plus fraction numerator left parenthesis straight n minus 1 right parenthesis over denominator 2 end fraction straight d close square brackets end style over denominator open square brackets straight A plus fraction numerator left parenthesis straight n minus 1 right parenthesis over denominator 2 end fraction straight D close square brackets end fraction equals fraction numerator 7 straight n minus 5 over denominator 5 straight n plus 17 end fraction
We space have space to space show space that space 6 to the power of th space terms space of space the space two space series space are space equal space then
fraction numerator begin display style left parenthesis straight n minus 1 right parenthesis end style over denominator begin display style 2 end style end fraction equals 5 rightwards double arrow straight n equals 11
fraction numerator begin display style 2 straight a plus 5 straight d end style over denominator begin display style 2 straight A plus 5 straight D end style end fraction equals fraction numerator 7 cross times 11 minus 5 over denominator 5 cross times 11 plus 17 end fraction equals 72 over 72 equals 1
Hence comma space the space 6 to the power of th space terms space of space the space two space series space are space equal.
end style

Answered by Sneha shidid | 28th Jan, 2019, 09:44: AM