If the general term formula of the equal ratio sequence is an = 2 ^ 4-N, then the sum of the first five terms of the sequence is

If the general term formula of the equal ratio sequence is an = 2 ^ 4-N, then the sum of the first five terms of the sequence is

an=2^(4-n)
a1=2^(4-1)=8
The common ratio is q = 2 ^ (- 1) = 1 / 2
Sn=a1*(1-q^n)/(1-q)=8*[1-(1/2)^n]/(1-1/2)=16(1-1/2^n)
S5=16(1-1/2^5)=31/2
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(1 / 2) 1. If the general term formula of the known sequence [an] is an = 2 ^ 2N-1, what are the first five terms and S5 of the sequence [an]? 2
(1 / 2) 1. Given that the general term formula of sequence [an] is an = 2 ^ 2N-1, what are the first five terms and S5 of sequence [an]?
2. It is known that the general term formula of the equal ratio sequence [an] is an = 2
(1 / 2) 1. In the equal ratio sequence [an], A3 = 7, the first three terms and S3 = 21, then what is the value of common ratio q?
2. If a1 + A4 = 1 (2 / 2) 8, A2 + a3 = 12, what is the sum of the first eight terms of the sequence [an]?

Solution 1s5 = a1 + A2 + a3 + A4 + A5
=2^2-1+2^4-1+...+2^10-1
=2^2+2^4+2^6+2^8+2^10-5
=1359
2 a3=a1*q²=7；
s3=(7*q-a1)/(q-1);
Sorting, 2 * Q & # 179; - 3 * Q & # 178; + 1 = 0;
By solving the equation, q = - 0.5 or q = 1

In known sequence an, A1 = 2, an + 1 = 1 / 2An, find the general term formula of sequence an, and find the sum S5 of the first five terms of sequence an

a(n+1)=1/2*an
a(n+1)/an=1/2
So an is an equal ratio sequence with the first term of 2 and the common ratio of 1 / 2
an=a1q^(n-1)
=2*(1/2)^(n-1)
=(1/2)^(n-2)
s5=a1(1-q^5)/(1-q)
=2*[1-(1/2)^5]/(1-1/2）
=(2*31/32)/(1/2)
=31/16*2
=31/8