It is known that {an} is an equal ratio sequence, and Sn is the sum of its first n terms. If A2 * A3 = 2A1, and the median of the difference between A4 and 2a7 is 5 / 4, then S5=

It is known that {an} is an equal ratio sequence, and Sn is the sum of its first n terms. If A2 * A3 = 2A1, and the median of the difference between A4 and 2a7 is 5 / 4, then S5=

∵ sequence {an} is equal ratio sequence, let the common ratio be Q
Then A2 * A3 = A1 * A4
∵a1*a4=2a1
∴a4=2
∵ A4 and 2a7 are 5 / 4
2*5/4=a4+2a7
∴a7=1/4
∵q³=a7/a4=1/8
∴q=1/2
∴a1=a4/q³=16
∴S5=a1*(1-q^5)/(1-q)=31
Hope to help you, welcome to ask:)

It is known that the sequence {an} is an equal ratio sequence, and Sn is the sum of its first n terms. If A2 &; A3 = 2A1, and the mean difference of A4 and 2a7 is 54, then S5 = ()
A．35 \x05\x05B．33 C．31 \x05D．29

c

It is known that the sequence {an} is an equal ratio sequence with A1 = 1, and {BN} is an equal difference sequence with the first term of 1, A5 + B3 = 21, A3 + B5 = 13
It is known that the sequence {an} is an equal ratio sequence of A1 = 1, {BN} is an arithmetic sequence with the first term of 1, A5 + B3 = 21, A3 + B5 = 13. ① find the general terms of {an} and {BN}, ② find the first n terms and Sn of {BN / 2An}

（1）A3＋B5=21＝1+2d+q^4
A5＋B3=13＝1+4d+q^2
So an = 1 + 2 (n-1) = 2N-1
Bn=2^(n-1)
（2）
Let CN = an / BN = (2n-1) / 2 ^ (n-1)
C1=1,C2=3/2,C3=5/4,C4=7/8
Sn=1+3/2+5/4+7/8+…… +(2n-3)/2^(n-2)+(2n-1)/2^(n-1)

The sequence {an} is an arithmetic sequence, {BN} is a positive proportional sequence, and A1 = B1 = 1, A3 + B5 = 21, A5 + B3 = 13. Find the general formula of {an} and {BN}

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