Question

Sum of first three terms of an ap is 42 and the product of first and third term is 52 . Find the first term and the common difference.

Answer 1

Hey mate here is ur answer ----

Let the AP be a+d, a, a-d

According to condition

a+d+a+a-d=42

3a=42

a=14

So the first terms is 14✓✓✓✓✓✓✓

(a+d) (a-d)=52

a²-d²=52

14²-d²=52

-d²=52-196

-d²=-144

d=12..

Common difference is 12 or -12

Hope its helps to u!!

❣️❣️

Answer 2

Let the three terms be a-d,a,a+d

Sum=a-d+a+a+d=42

3a=42

a=14----------(1)

Next,

product=(a-d)(a+d)=52

SUBSTITUTE a=14

(14-d)(14+d)=52

196-d^2=52

-d^2=52-196

d^2=144

d=+ or - 12-----(2)

From 1 and 2

a=14 , d=+12/-12