Question

sum of first 3 term of an ap is 48 if product of first and second term exceeds for time the third term by 12 find the AP​

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

First term be p

Also

Common difference be d

Sum of First term

p - d + p + p + d = 48

3p = 48

$\tt{\rightarrow p=\dfrac{48}{3}}$

p = 16

Also it is given that :-

Product of first and second term exceeds for time the third term by 12

${\boxed{\sf\:{Situation}}}$

(p - d)p = 4(p + d) + 12

${\boxed{\sf\:{Substitute\;the\;value\;of\;p}}}$

(16 - d)16 = 4(16 + d) + 12

256 - 16d = 64 + 4d + 12

256 - 16d = 76 + 4d

256 - 76 = 4d + 16d

180 = 20d

$\tt{\rightarrow\dfrac{180}{20}=d}$

9 = d

Therefore we get :-

p - d = 16 - 9 = 7

p = 16

p + d = 16 + 9 = 25

$\Large{\boxed{\sf\:{AP=7,16,25}}}$