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What is the 7th term of the geometric sequence where a1 = 256 and a3 = 16?
Solution:
The nth term of the geometric sequence is given by:
an = a · rn - 1,
Where a is the first term and r is the common ratio respectively.
Given: a1 = a = 256 and a3 = 16
We know, an = a · rn - 1
⇒ a3 = a. r3 - 1
⇒ 16 = 256 × r2
⇒ r2 = 16/256
⇒ r2 = 1/16
⇒ r = ±1/4
Now, a7 = a. r7 - 1 = a . r6
⇒ a7 = 256 × (1/4)6
⇒ a7 = 256/4096
⇒ a7 = 1/16
If r = -1/4, then
⇒ a7 = 256 × (-1/4)6
⇒ a7 = 256/4096
⇒ a7 = 1/16
Therefore, the 7th term of the geometric sequence a7 is 1/16.
What is the 7th term of the geometric sequence where a1 = 256 and a3 = 16?
Summary:
The 7th term of the geometric sequence where a1 = 256 and a3 = 16 is 1/16.
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