Question

if a1,a2,a3,..... are in A.P such that a4/a7=3/2, then find the 13th term of the A.P

Answer 1

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Answer 2

Answer:

The 13th term of the A.P is 0.

Step-by-step explanation:

It is given that if a1, a2, a3,..... are in A.P, then

$\frac{a_4}{a_7}=\frac{3}{2}$

The nth term of an AP is

$a_n=a+(n-1)d$

$\frac{a+(4-1)d}{a+(7-1)d}=\frac{3}{2}$

$\frac{a+3d}{a+6d}=\frac{3}{2}$

$2(a+3d)=3(a+6d)$

$2a+6d=3a+18d$

$0=3a+18d-2a-6d$

$0=a+12d$

$0=a+(13-1)d$

$0=a_{13}$

Therefore the 13th term of the A.P is 0.