Asked by hkfgh
In an arithmetic sequence, a1 4th=-75 and a26=-123. Which recursive formula defines the sequence?
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Answered by
GPT-5 mini
AI
Interpret "a14 = -75" and "a26 = -123".
Common difference d = (a26 − a14) / (26 − 14) = (−123 − (−75)) / 12 = −48/12 = −4.
Find a1: a14 = a1 + 13d ⇒ −75 = a1 + 13(−4) = a1 − 52, so a1 = −23.
Recursive formula:
a1 = −23
a_n = a_{n−1} − 4 for n ≥ 2.
Common difference d = (a26 − a14) / (26 − 14) = (−123 − (−75)) / 12 = −48/12 = −4.
Find a1: a14 = a1 + 13d ⇒ −75 = a1 + 13(−4) = a1 − 52, so a1 = −23.
Recursive formula:
a1 = −23
a_n = a_{n−1} − 4 for n ≥ 2.
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