Question

The ratio of 6th and 8th term of an A.P. is 7:9.Find the ratio of 9th term to 13th term.​

Answer 1

Answer :-

5:7

Given :-

• Ratio of 6th term and 8th term of an A.P is 7:9

To find :-

• Ratio of 9th term to 13th term

Solution:-

As they given that ,

6th term / 8th term = 7/9

a₆/ a₈ = 7/9 ----- eq -1

So, 6th term will be the

As we know that ,

aₙ = a+(n-1)d

• n is nth term
• a is first term
• d is common difference

a₆ = a+(6-1) d

a₆ = a + 5d

Similarly,

a₈ = a+(8-1) d

a₈ = a+ 7d

Substituting the values in equation 1

a₆/ a₈ = 7/9

(a+5d)/(a+7d) = 7/9

Do cross multiplication

(a+5d)9 = (a+7d)7

9a + 45d = 7a + 49d

9a -7a = 49d -45d

2a = 4d

a = 2d

We need to find the 9th term/13th term ratio i.e

a₉ : a₁₃

Similarily

a₉ = a+(9-1) d

a₉ = a+8d

a₁₃ = a+(13-1)d

a₁₃ = a+ 12d

Now,

a₉ / a₁₃ = (a+8d)/(a+12d)

We know that a=2d

Substitute there

a₉ / a₁₃ = [2d +8d] / [2d+12d]

a₉ / a₁₃ = (10d)/(14d)

a₉ / a₁₃ = 10/14

a₉ / a₁₃ = 5/7

a₉ : a₁₃ = 5:7

So, the ratio of 9th term to 13th term is 5:7