How do you write the expression for the nth term of the geometric sequence a_4=-18, a_7=2/3, n=6?
1 Answer
Mar 5, 2017
Explanation:
"The nth term for a geometric sequence is"
• a_n=ar^(n-1)" where a is the 1st term" To obtain the nth term for the given sequence, we require to find a and r.
"Given " a_4=-18" and "a_7=2/3" then"
rArra_4=ar^3=-18to(1)
rArra_7=ar^6=2/3to(2)
rArr(ar^6)/(ar^3)=(2/3)/(-18)
rArrr^3=-1/27rArrcolor(red)(r=-1/3)
"From (1) " ar^3=-18
rArra=(-18)/(-1/27)rArrcolor(red)(a=486)
rArr"nth term expression is " a_n=486(-1/3)^(n-1)
