Question

If 18, a,(b-3) are in AP then a+ b is ____

plz solve it ​

Answer 1

• Let 18 , a , b-3 are in A.P

• Here

$\sf \: a_{1} = 18$

$\sf a_{2} = a$ ( here a is not first term it's an variable)

$\sf a_{n} = b - 3$

• Then Common Difference

$\sf d = a_{2} - a_{1}$

$\sf d = a - 18$

• Similarly

$\sf \: a_{n} = a + (n - 1)d$

$\sf a_{3} = 18+ (3- 1)a - 18$

$\sf a_{3} = \cancel18+ (2)a - \cancel18$

$\sf a_{3} =2a \:\:\:\:\: here \: a = 18$

$\sf \: a_{3} = 2 \times 18$

$\sf a_{3}= 54$

Therefore

b - 3 = 54

b = 54 + 3

b = 57

To Find a (Middle term)

We know that $\sf \frac{a + c}{2}$

$\sf = \frac{18 + 54}{2}$

$\sf = \frac{72}{2}$

$\sf a = 36$(here a is not first term it's an variable)

Therefore a = 36 & b = 57

Then a + b = 36 + 57 = 93