How do you write an expression for the nth term of the geometric sequence with a1=64, r=-1/2, and n=10? Find the indicated term.

1 Answer
Teddy
Jun 25, 2018

#a_n=64(-1/2)^(n-1)#, so #a_10=64(-1/2)^9=-1/8#

Explanation:

The explicit formula for the #n^"th"# term of a geometric sequence with first term #a_1#, common ration #r# is #a_n=a_1r^(n-1)#. Since we are given the values of #a_1# and #r#, we have the formula for the #n^"th"# term of the sequence: #a_n=64(-1/2)^(n-1)#. To find the #10^"th"# term, we just substitute #n=10# into the formula and get #a_10=64(-1/2)^9=-1/8#.

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