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zepelin [54]
3 years ago
12

20 The nth term of an arithmetic series is Un where un > 0 for all n.

Mathematics
1 answer:
Kruka [31]3 years ago
3 0

Answer:

Hi,

u_{20}=30

Step-by-step explanation:

u_n=u_1+(n-1)*r, \ r= commun\ ratio.\\u_4=u_1+3*r=6\\u_6=u_1+5r\\(u_6)^2=u_1^2+10ru_1+25r^2\\s_n=u_1+u_1+r+u_1+2r+...+u_1+10r=11*u_1+55r\\s_{11}=(u_6)^2+18\ \\\Longrightarrow\ u_1^2+10ru_1+25r^2+18=11u_1+55r\\\Longrightarrow\ 4r^2+2r-12=0\\\Longrightarrow\ 2r^2+r-6=0\\r=\dfrac{3}{2} \ or\ r=-2\ (excluded)\\\\u_1=6-3r=\dfrac{3}{2} \\\\\\\boxed{u_{20}=u_1+19*r=30}\\

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