Question

If the first three terms of an AP are 9p, 4q
and 7p, then find the ratio of p and q.​

Answer 1

Answer:

first term of an a.p = a = 9p

second term of an a.p = a + d = 4q

third term of an a.p = a + 2d = 7p

according to the question

a = 9p equation 1

a + d = 4q equation 2

a + 2d = 7p equation 3

subtracting equation 2 from equation 3

d = 7p - 4q

putting value of d and a in equation 2

9p + 7p - 4q = 4q

16p = 8q

p / q = 8 / 16

p / q = 1 / 2

=> 1 : 2

hope it helps you

Answer 2

Answer :–

• The ratio of p and q is 1:2

Given :–

• If the first three terms of an AP are 9p, 4q and 7p.

To Find :–

• Find the ratio of p and q.

Solution :–

If an arithmetic progression (A.P.),

→ a, b, c.

then,

→ 2b = a + c ---------- (1)

Given that,

• a = 9p
• b = 4q
• c = 7p

Put this values on (1), we obtain

→ 2(4q) = 9p + 7p

→ 8q = 16p

→ q = 16p/8

→ q = 2p

• q = 2

It means,

• p = 1

because there is no numerator so we will take 1 as a numerator.

Now, turn p to the left side and divide by q.

→ 1/2 = p/q

ATQ,

We need to find the ratio of p and q.

So, the ratio is,

• 1:2