Question

the 12th term of an arithmetic sequence is 29. if the 3rd term is subtracted from the 7th term the result is -8. what is the 52nd term?

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Answer 1

Answer:

-51

Step-by-step explanation:

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Given :-

the 12th term of an arithmetic sequence is 29. if the 3rd term is subtracted from the 7th term the result is -8.

To Find :-

52nd term

Solution :-

We know that

${\large{\boxed{\underline{\bf a_n=a+(n-1)d}}}}$

$\sf :\implies a_{12}=a+(12-1)d$

$\sf :\implies 29=a+11d$

$\sf :\implies 29-11d=a(..1)$

now,

A/q

$\sf :\implies a_7-a_3=-8$

$\sf :\implies a+(7-1)d-[a+(3-1)d]=-8$

$\sf :\implies a+6d-[a+2d]=-8$

$\sf :\implies a+6d-a-2d=-8$

$\sf :\implies 4d=-8$

$\sf :\implies d=\dfrac{-8}{4}$

$\sf :\implies d=-2$

From 1

$\sf :\implies 29 -11(-2)=a$

$\sf :\implies 29-(-22)=a$

$\sf :\implies 29+22=a$

$\sf :\implies 51=a$

Finding 52th and

$\sf :\implies a_{52}=a+(52-1)d$

$\sf :\implies a_{52}=51+(51)\times(-2)$

$\sf :\implies a_{52}=51+(-102)$

$\sf :\implies a_{52}=-51$