If the 4th term ofan A.P. is 7 and the 7th term
is 4 show that the 11th term 0.
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By the given,
⇒ 4th term is 7,
a+(4-1)d=7
a+3d=7 ...(1)
⇒ 7th term is 4 ,
a+(7-1)d=4
a+6d=4 ....(2)
subtract eqn 1 and 2,
a+3d-a-6d= 7-4
-3d=3
→d=(-1)
substitute d in eqn 1,
a+3(-1)=7
a=7+3
→a=10
now, aₙ=a+(n-1)d
a₁₁=10+(11-1)(-1)
a₁₁=10-10
∴a₁₁=0
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