Determine the AP whose third term is 16 and the 7^ th term exceed… - Vidyadip

Question

Determine the AP whose third term is $16$ and the $7^{th}$ term exceeds the $5^{th}$ 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$
$4, 10, 16....$

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