The third term of a geometric sequence is 64 and the eighth term is -2,048. What is the first term?
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2
Answer:
16
Step-by-step explanation:
Let the first term be a and the common ratio r
Use the formula for the n'th term: xn = arn - 1
The third term = 64 ⇒ x3 = ar3 - 1 = 64 ⇒ ar2 = 64 (1)
The eighth term = -2,048 ⇒ x8 = ar8 - 1 = -2,048 ⇒ ar7 = -2,048 (2)
Divide (2) by (1)⇒ r5 = -2,048/64 = -32 ⇒ r = -2
Substitute r = -2 into (1) ⇒ a × (-2)2 = 64 ⇒ a × 4 = 64 ⇒ a = 64 ÷ 4 =16
The first term is 16
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