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ellomlysia
:
the sum of the first term and seventh term of an arithmetic progression is 16. if the twentieth term is 56, find the term whose value first exceeds 1000.
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January 11, 2015 at 12:54pm
Shu Yun
:
[deqn]U_{n}=a+(n-1)d\\ U_{1}=a; ~U_{7}=a+(7-1)d\\ U_{1}+U_{7}=a+a+(7-1)d=16\\ 2a+6d=16\rightarrow eqn(1)\\ U_{20}=a+(20-1)d=56\\ a+19d=56\rightarrow eqn(2)\\ Solving~eqns~(1)~and~(2),\\a=-1,d=3 \\Then,U_{n}\gt1000\\ a+(n-1)d\gt1000 \\-1+(n-1)(3)\gt1000 \\n\gt334.667\\n=335(ans)[/deqn]
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January 17, 2015 at 11:43pm
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