How do you find the explicit formula for the following sequence 10, 12.5, 15, 17.5,...?

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Answer 1 · 2016-03-25T09:40:28

#n^(th)# term is #(7.5+2.5n)# and
sum of the series up to #n^(th)# term is #n/2(17.5+2.5n)#

The sequence #10, 12.5, 15, 17.5,...# is arithmetic sequence with first term #a=10# and common difference #d=12.5-10=2,5#

In an arithmetic sequence #{a,a+d,a+2d,a+3d,.......}#

#n^(th)# term is given by

#a+(n-1)d=10+(n-1)2.5=10+2.5n-2.5=(7.5+2.5n)#

Sum of the series up to #n^(th)# term is given by

#n/2(2a+(n-1)d)=n/2(2*10+(n-1)*2.5# or

#n/2(20+2.5n-2.5)# or #n/2(17.5+2.5n)#