急! F6 Geometric Sequences 02q3

14.
(a)
The geometric sequence
= T1, T2, T3, T4......
= T1, T1r, T1r², T1r³......

aT1, aT2, aT3, aT4......
= (aT1), (aT1)r, (aT1)r², (aT1)r³......

Hence, the sequence is a geometricsequence.
The common ratio = r

(b)
T1-b, T2-b, T3-b, T4-b,......
= T1-b, T2-b, T3-b, T4-b......
= T1-b, T1r-b, T1r²-b,T1r³-b......

(T1r-b)/(T1-b) ≠ (T1r²-b)/(T1r-b)≠ (T1r³-b)/(T1r²-b)
Hence, the sequence is NOT ageometric sequence.

(c)
= aT1/b, aT2/b, aT3/b, aT4/b, ......
= (aT1/b), (aT1/b)r, (aT1/b)r², (aT1/b)r³, ......

Hence, the sequence is a geometricsequence.
The common ratio = r


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15.
The geometric sequence
= T1, T2, T3, T4......
= T1, T1r, T1r², T1r³......

(T1+k)/k, (T2+k)/k, (T3+k)/k, (T4+k)/k,......
= (T1+k)/k, (T1r+k)/k, (T1r²+k)/k,(T1r³+k)/k, ......

[(T1r+k)/k] / [(T1+k)/k] = (T1r+k) / (T1+k)
[(T1r²+k)/k] / [(T1r+k)/k] = (T1r²+k)/ (T1r+k)
[(T1r³+k)/k] / [(T1r²+k)/k]= (T1r³+k) / (T1r²+k)

[(T1r+k)/k] / [(T1+k)/k] ≠ [(T1r²+k)/k]/ [(T1r+k)/k] ≠ [(T1r³+k)/k]/ [(T1r²+k)/k]
Hence, the sequence is NOT ageometric sequence.