Question
Determine the AP whose third term is 16 and the $7^{\text {th }}$ term exceeds the $5^{\text {th }}$ term by 12 .
✓
Answer
$a_3 = 16$
$ \Rightarrow a + 2d = 16 ..... (i)$
$a_7 = a_5 + 12$
$ \Rightarrow a + 6d = a + 4d + 12$
$ \Rightarrow 2d = 12$
$ \Rightarrow d = 6$
Put the value of d in eq. (i)
$a + 2 \times 6 = 16$
$ \Rightarrow a = 16 - 12$
$ \Rightarrow a = 4$
$4, 10, 16....$
$ \Rightarrow a + 2d = 16 ..... (i)$
$a_7 = a_5 + 12$
$ \Rightarrow a + 6d = a + 4d + 12$
$ \Rightarrow 2d = 12$
$ \Rightarrow d = 6$
Put the value of d in eq. (i)
$a + 2 \times 6 = 16$
$ \Rightarrow a = 16 - 12$
$ \Rightarrow a = 4$
$4, 10, 16....$
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