Question

the ratio of 11th term and the 18th term of an arithmetic progression is 2 is to 3 find the ratio of 5th term to the 21st term and also the ratio of the sum of first 5 terms to the sum of first 21 pounds ​

Answer 1

$\huge{\boxed{\underline{\bold{ \bigstar{answer}}}}}$

(a + 10d)/(a + 17d) = 2/3

(a + 10d)/(a + 17d) = 2/3

3a + 30d = 2a + 34d

3a - 2a = 34 - 30 

a = 4d

a₅ = a + 4d

= 4d + 4d 

a₅ = 8d

a₂₁ = a + 20d

= 4d + 20d

a₂₁ = 24d

So, a₅ : a₂₁ = 8 : 24 = 1 : 3

The ratio of the sum of the first 5 terms to the sum of the first 21 terms.

S₅ = 5/2(8d + 4d)

= 60d/2

S₅ = 30d

S₂₁ = 21/2(8d + 20d)

= 588d/2

S₂₁ = 294d

So, 

S₅ : S₂₁ = 30d : 294d

 = 5 : 49

hope it helps you....