Question

The 11th term and the 21th term of an A.P are 16 and 29 respectively ,then find the 41th term of that A.P
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Answer 1

Let a and d respectively be the first term and common difference of the A.P.

a₁₁=16 (Given)

⇒a+10d=16 ...(1)

( Using:aₙ=a+(n-1)d )

a₂₁=29 (Given)

⇒a+20d=29 ...(2)

( Using:aₙ=a+(n-1)d )

Subtracting eq.(1) from eq.(2),

a+20d-a-10d=29-16

⇒10d=13

⇒d=13/10

⇒d=1.3

Putting d=1.3 in eq.(1),

a+10(1.3)=16

⇒a+13=16

⇒a=3

Now,

a₄₁=a+40d ( Using:aₙ=a+(n-1)d )

⇒a₄₁=3+40(1.3)

⇒a₄₁=3+52

⇒a₄₁=55