Algebra sequences & series?
I've learned all the formulas for these. Nonetheless, I encountered several problems that appears to be irrelevant from the rest. Here is one I am working on:
a(subscript: 1)= 4 ; a(subscript: k+1) = 3/2a(subscript:k) - 2
It asked if the sequence is arithmetic, geometric, or none. Regardless of the answer, I need to know what formula or steps I first start with? Are these series and sequences done in a different style?
Comments
a1 = 4 means first term = 4
a(k + 1) = 3/2 a(k) -- 2 means (k+1)th term is obtained from kth term by this formula.
a(2) = 3/2a(1) -- 2 = 3/2(4) -- 2 = 4
and this repeats indefinitely so the series is
4, 4, 4, 4, 4, 4, which can be
named arithmetic with common difference 0,
or geometric series with common ratio 1 or
harmonic series with inverse common difference 0.