Question

等比数列（An)前n项和为Sn,S5=2,S10=6,则A16加到A20等于多少?

Answer 1

S5,S10,S15,S20不成等比

S5=a1(q^5-1)/(q-1)=2

S10=a1(q^10-1)/(q-1)=6

S10/S5=6/2=3

=(q^10-1)/(q^5-1)=q^5+1

q^5=2

S15=S5*(q^15-1)/(q^5-1)

=2(2^3-1)/(2-1)

=2*7=14

S20=S5*(q^20-1)/(q^5-1)

=2*(2^4-1)/(2-1)

=2*15=30

所以,A16加到A20=S20-S15=30-14=16