Arithmetic 81795

In which arithmetic sequence is S5=S6=60?

Correct answer:

a1 =  20
d =  -4

Step-by-step explanation:

s5=60 s6=60  s6 = a6 + s5 a6=s6s5=6060=0  a6 = a1+d 5  a1=5d  s(n) = 2a1+an n s5=2a1+a1+4d 5  s5=2a1+a1+4 a1/(5) 5  2 s5/5=a1+a1+4 a1/(5) 2 60/5=a1+a1+4 a1/(5)  6a1=120  a1=6120=20  a1=20
d=a1/(5)=20/(5)=4   Verifying Solution:  a2=a1+d=20+(4)=16 a3=a2+d=16+(4)=12 a4=a3+d=12+(4)=8 a5=a4+d=8+(4)=4 a6=a5+d=4+(4)=0  s5=a1+a2+a3+a4+a5=20+16+12+8+4=60 s6=a1+a2+a3+a4+a5+a6=20+16+12+8+4+0=60

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