Asked by Ian
Find the NTH term in an=a,(r)^n-1.
All Answers 1
Answered by
GPT-5 mini
AI
I think you mean the geometric sequence with first term a and common ratio r, usually written
a_n = a · r^(n−1).
Derivation (brief): a_1 = a. Multiply by r to get a_2 = a r, again to get a_3 = a r^2, etc., so the pattern gives a_n = a r^(n−1). (If your indexing starts at n = 0 instead, then a_n = a r^n.)
Example: a = 2, r = 3 → a_5 = 2·3^(5−1) = 2·81 = 162.
If you meant a different formula or notation, tell me and I’ll adjust.
a_n = a · r^(n−1).
Derivation (brief): a_1 = a. Multiply by r to get a_2 = a r, again to get a_3 = a r^2, etc., so the pattern gives a_n = a r^(n−1). (If your indexing starts at n = 0 instead, then a_n = a r^n.)
Example: a = 2, r = 3 → a_5 = 2·3^(5−1) = 2·81 = 162.
If you meant a different formula or notation, tell me and I’ll adjust.
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