Question

if 4, a,b,28 are in Ap find the value of b​

Answer 1

Step-by-step explanation:

We know that, in an AP common difference is same,

$d_1 = a_2-a_1= a_3-a_2$

$\implies \: a - 4 = b - a$

$\implies2a = b + 4 \: \: \: \: \: \: \: \:$

$\implies \: a = \frac{b + 4}{2} \: \: \: \: \: \: \: \: \: \: \: \: (1)$

$d_2 = a_4-a_3= a_3-a_2$

$\implies28 - b = b - a$

$\implies2b = 28 + a$

Now putting value of a in equation 2

$\implies2b = 28 + \frac{b + 4}{2}$

$\implies2b = \frac{56 + b + 4}{2}$

$\implies4b = 60 + b$

$\implies4b - b = 60$

$\implies3b = 60$

$\implies{b = \frac{60}{3} }$

$\implies{\boxed{b = 20}}$

Now put the value of b in equation 1

$\implies \: a = \frac{20 + 4}{2}$

$\implies \: a = \frac{24}{2}$

$\implies \: \boxed{ a= 12}$

Hence the values of a and b is 12 and 20 respectively.