Math

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1. What is the tenth term of the geometric sequence whose first term (a1) is 16 and the common ratio (r) is –½?

2. Given the terms a10 = 3 / 512 and
a15 = 3 / 16384 of a geometric sequence, find the exact value of the first term of the sequence.

• Math -

1
term(n) = ar^(n-1)
term(10) = 16(-1/2)^9
= 16(-1/512)
= - 1/32

2.
ar^9 = 3/512
ar^14 = 3/16384
divide the 2nd by the first
r^5 = 1/32
r = 1/2
back into the first

a(1/2)^9 = 3/512
a(1/512) = 3/512
a = 3(512)/512 = 3

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