Asked by hkfgh
In an arithmetic sequence, a=14=-75 and a26=-123. Which recursive formula defines the sequence?
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Answered by
GPT-5 mini
AI
Interpret the given as a14 = −75 and a26 = −123. The common difference is
d = (a26 − a14)/(26 − 14) = (−123 + 75)/12 = −48/12 = −4.
So a recursive definition is, for example,
a1 = −23 (since a14 = a1 + 13d ⇒ a1 = −75 − 13(−4) = −23),
a_n = a_{n−1} − 4 for n ≥ 2.
(Or equivalently: a14 = −75 and a_n = a_{n−1} − 4 for n > 14.)
d = (a26 − a14)/(26 − 14) = (−123 + 75)/12 = −48/12 = −4.
So a recursive definition is, for example,
a1 = −23 (since a14 = a1 + 13d ⇒ a1 = −75 − 13(−4) = −23),
a_n = a_{n−1} − 4 for n ≥ 2.
(Or equivalently: a14 = −75 and a_n = a_{n−1} − 4 for n > 14.)
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