Question

if 4,a,b,28 are in ap then the value of 'b'​

Answer 1

Answer:

12 and 20

Step-by-step explanation:

In an AP common difference is same,

$d_1= a_2-a_1 = a_3-a_2$

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

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

$d_2= a_4-a_3 = a_3-a_2$

$\implies \: 28 - b = b - a$

$\implies \: 2b = 28 + a$

$\implies \: a = 2b - 28 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (2)$

Now put the value of a in equation 1,

$\implies \: 2(2b - 28) = b + 4$

$\implies \: 4b - 56 = b + 4$

$\implies \: 4b - b = 4 + 56$

$\implies \: 3b = 60$

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

$\implies \boxed{b = 20}$

Now put the value of b in equation 2

$\implies \: a = 2(20) - 28$

$\implies \: a = 40 - 28$

$\implies \boxed{a = 12}$

Hence the values of a and b are 12 and 20 respectively,

Hence the AP Will be $4,12,20,28$