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OpenStudy (anonymous):
Write the first five terms of the arithmetic sequence. Find the common difference and write the nth term of the sequence as a function of n. a1 = 0.375, ak+1 = ak +0.25
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OpenStudy (anonymous):
replace k by natural numbers 2, 3, 4, 5 just like you would with a function. for example \[a_2=a_1+0.25=0.375+0.25=.625\] etc
OpenStudy (anonymous):
first step in "etc" is \[a_3=a_2+0.25+.625+.25=.875\]
OpenStudy (anonymous):
"common difference" is evidently 0.25 because that is what you are adding to each successive term. so \[a_n=0.375+(n-1)\times 0.25\]
OpenStudy (anonymous):
you can do some algebra to get \[a_n=0.375+n\times 0.25-0.25=0.125+0.25n\]
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