For an AP show that Tp+2q equal 2Tp+q

1.	For an AP show that Tp+2q equal 2Tp+q
Answer» Let the first term be a and the common difference be d.we know,\xa0{tex}a_n= a+(n-1)d{/tex}{tex}a_p=a+(p-1)d{/tex}{tex}a_{p+2q}=a+(p+2q-1)d{/tex}\xa0{tex}\\therefore a_p+a_{p+2q}=a + (p - 1)d + a + (p + 2 q -1)d{/tex}{tex}= a + pd - d + a + pd + 2qd - d{/tex}{tex}= 2a + 2pd + 2qd - 2d{/tex}{tex}= 2[a + (p + q - 1) d]{/tex} ............(i){tex}2a_{p+q}=2[a + (p + q - 1 ) d ]{/tex}\xa0..........(ii)From (i) and (ii), we getap + ap + 2q\xa0= 2ap+q

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