Question

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

Answer 1

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

Answer 2

first step in "etc" is
\[a_3=a_2+0.25+.625+.25=.875\]

Answer 3

"common difference" is evidently 0.25 because that is what you are adding to each successive term. so
\[a_n=0.375+(n-1)\times 0.25\]

Answer 4

you can do some algebra to get
\[a_n=0.375+n\times 0.25-0.25=0.125+0.25n\]