Question

Finda,bsuchthat 7.2, a, b, 3 are in A.P.​

Answer 1

Answer:

• The value of a = 5.8

• The value of b = 4.4

Step-by-step explanation:

Given

7.2, a, b, 3 are in A.P

$2a = 7.2+b$

$b = 2a - 7.2$

as

a, b, 3 are also in A.P

$2b\:=\:a\:+\:3$

Putting $b = 2a - 7.2$

$2\left(2a-7.2\right)=a+3$

$4a-14.4=a+3$

$\mathrm{Add\:}14.4\mathrm{\:to\:both\:sides}$

$4a-14.4+14.4=a+3+14.4$

$4a=a+17.4$

$4a-a=a+17.4-a$

$3a=17.4$

$\mathrm{Divide\:both\:sides\:by\:}3$

$\frac{3a}{3}=\frac{17.4}{3}$

$a=5.8$

Now, plugging $a=5.8$ in $b = 2a - 7.2$

$b=2\left(5.8\right)-7.2$

$b=2\cdot \:5.8-7.2$

$b=11.6-7.2$

$b=4.4$

Therefore,

• The value of a = 5.8

• The value of b = 4.4