How do you write a rule for the nth term of the arithmetic sequence and then find #a_22# given #d=3.8, a_8=76.4#?

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Answer 1 · 2017-06-21T14:55:15

#n^(th)# term is #3.8n+46# and #a_22=129.6#

In an arithmetic sequence, whose first term is #a_1# and common difference is #d#, #n^(th)# term is given by

#a_n=a_1+(n-1)xxd#

As #a_8=76.4#, #8^(th)# term is #76.4# or

#76.4=a_1+(8-1)xx3.8#

or #76.4=a_1+26.6# and #a_1=76.4-26.6=49.8#

and #n^(th)# term is #49.8+(n-1)xx3.8=3.8n+49.8-3.8=3.8n+46#

hence #a_22=3.8xx22+46=83.6+46=129.6#