Sam wants to create an arithmetic sequence and a geometric sequence, both of which have t(1)=8 and t(7)=512. Is this possible? If it is, help Sam create his sequences. If not, justify why not.How do I do this?

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Answer 1 · 2018-02-09T02:41:45

Yes.

.

In an arithmetic sequence, we have:

#t(7)=t(1)+(t-1)d#

#512=8+(7-1)d#

#512=8+6d#

#504=6d#

#d=84#

Common difference is #84#.

In a geometric sequence, we have:

#t(7)=t(1)r^(t-1)#

#512=8r^(7-1)#

#512=8r^6#

#r^6=512/8#

#r^6=64#

#r=2#

Common ratio is #2#.

Yes, it is possible.