a3×a6×a15=a1³q^21=(a1q^7)³是常數(shù),則a1q^7是常數(shù).
Tn=a1ⁿ×q^[1+2+...+(n-1)]
=a1ⁿ×q^[n(n-1)/2]
=(a1q^7)ⁿ×q^[n(n-1)/2 -7n]
=(a1q^7)ⁿ×q^[n(n-15)/2]
a1q^7是常數(shù),(a1q^7)ⁿ是常數(shù),要Tn是常數(shù),只有q^[n(n-15)/2]是常數(shù),q是變量,只有q的0次方=1,是常數(shù).
n(n-15)/2=0
n(n-15)=0
n=0(n是正整數(shù),舍去)或n=15
只有T15是常數(shù).