In a certain AP the 24term term is twice the10term .prove that 72term

1.	In a certain AP the 24term term is twice the10term .prove that 72term is twice the 34 term
Answer» Given,a24\xa0= 2{tex}\\times{/tex}\xa0a10{tex}\\Rightarrow{/tex}\xa0a + (24\xa0- 1)d = 2{tex}\\times{/tex}[a + (10 - 1)d]{tex}\\Rightarrow{/tex}a + 23d = 2[a + 9d]{tex}\\Rightarrow{/tex}a + 23d = 2a + 18d{tex}\\Rightarrow{/tex}a - 2a = 18d - 23d{tex}\\Rightarrow{/tex}-a = -5d{tex}\\Rightarrow{/tex}a = 5d...........(i)To prove: a72\xa0= 2a34Proof:LHS = a72= a + (72\xa0- 1)d= 5d\xa0+ 71d [From (i)]= 76dRHS = 2a34= 2[a + (34\xa0- 1)d]= 2[5d + 33d]= 2\xa0{tex}\\times{/tex}38d= 76d{tex}\\therefore{/tex} LHS = RHS

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