How do you write the nth term rule for the arithmetic sequence with #d=-4.1# and #a_16=48.2#?

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Answer 1 · 2017-03-17T06:31:08

#a_n=113.8-4.1xxn#

In an arithmetic sequence, whose first term is #a_1# and common difference is #d#, the #n^(th# term #a_n# is given by #a_n=a_1+(n-1)d#

As #a_16=48.2# and #d=-4.1#, we should have

#48.2=a_1+(16-1)xx(-4.1)#

or #48.2=a_1+15xx(-4.1)#

or #48.2=a_1-61.5#

and #a_1=48.2+6.5=109.7#

Hence #n^(th# term rule for #a_n# is #a_n=a_1+(n-1)d#

i.e. #a_n=109.7+(n-1)xx(-4.1)=109.7-4.1xxn+4.1#

i.e. #a_n=113.8-4.1xxn#