Question

Let a,b,c are in G.P. and 4a,5b,4c are in A.P. such that a+b+c=70 , then value of b is:

Answer 1

Answer:

The value of b = 20

Step-by-step explanation:

Given that a, b, c is in G.P., so we can get

b² = ac ………... (i)

Again, we have been given that 4a, 5b, 4c is in A.P., so it will become

2b = a + c

here, a = 4a, b = 5b and c = 4c

therefore, 2 * 5b = 4a + 4c

Or, 10b = 4a + 4c ……… (ii)

Dividing the equation (ii) by 2

Or, 5b = 2a + 2c ………………………. (iii)

We have, a + b + c = 70 ………(iv)

Multiplying 2 on both sides of the equation (iv)

2a + 2b + 2c = 140

Or, 2b + 5b = 140 ……… (from equation (iii))

Or, 7b = 140

Or, b = 140/7 = 20

or, b = 20

From equation (i) we get

(20)² = ac ......(since b=20)

or, 400 = ac .........(v)

now, from equation (iv)

a + 20 + c = 70

or, a + c = 50 ........(vi)

Therefore, (a - c)² = (a + c)² - 4ac = 2500 - 4*400 = 900

or, a - c = ±30 .......(vii)

Taking a - c = 30 and solving with equation (vi), we get

a = 40 and c = 10

or, Taking a - c = -30 and solving with equation (vi), we get

a = 10 and c = 40