The sum of the fifth term and twice the third of an arithmetic sequence equals the twelth term. if the seventh term is 25 find an expression for the general term
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a₅+2a₃=a₁₂
a+4d+2(a+2d)=a+11d
3a+8d=a+11d
2a=3d
d=2a/3
a₇=a+6d
25=a+6(2a/3)
a+4a=25
a=25/5
a=5
d=2(5)/3
d=10/3
aₓ=a+(x-1)d
=5+(x-1)(10/3)
=5+(10x/3)-(10/3)
=(10/3)x + (5/3)
a+4d+2(a+2d)=a+11d
3a+8d=a+11d
2a=3d
d=2a/3
a₇=a+6d
25=a+6(2a/3)
a+4a=25
a=25/5
a=5
d=2(5)/3
d=10/3
aₓ=a+(x-1)d
=5+(x-1)(10/3)
=5+(10x/3)-(10/3)
=(10/3)x + (5/3)
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