Determine the A.P. whose third term is 16 and the 7th term exceed… - Vidyadip

Question

Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12

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Answer

$
\begin{aligned}
& T _3=16 \\
& T _7- T _5=12
\end{aligned}
$
Let $a$ be the first term and $d$ be the common difference
$
\begin{aligned}
& T_3=a+2 d=16 ......(1)\\
& T_7-T_5=(a+6 d)-(a+4 d)=12 \\
& \Rightarrow a+6 d-a-4 d=12 \\
& \Rightarrow 2 d=12 \\
& \Rightarrow d=\frac{12}{2}=6
\end{aligned}
$
Substitute the value of $d$ in eq. (i), we get
$
\begin{aligned}
& \therefore a+2 \times 6=16 \\
& \Rightarrow a+12=16 \\
& \Rightarrow a=16-12=4 \\
& \therefore \text { A.P. is } 4,10,16,22,28, \ldots
\end{aligned}
$

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