Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds … - Vidyadip

Question

Determine the A.P. Whose $3$rd term is $16$ and the $7$th term exceeds the $5$th term by $12.$

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Answer

For given A.P
$t_3=a+2 d=16 \ldots$..(i)
Now
$t_7-t_5=12$
$\Rightarrow(a+6 d)-(a=4 d)=12$
$\Rightarrow 2 d =12$
$\Rightarrow d =6$
Substituting the value of din $(i)$ we get
$a+2 \times 6=16$
$\Rightarrow a+12=16$
$\Rightarrow a=4$
Thus the required A.P $= a, a + d, a + 2d, a + 3d,....$
$= 4, 10, 16, 22,.....$

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