The ratio of the 11th term and 18th term of an A.P. os 2:3.Find the ratio of the 5th term and 21st term.
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(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
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
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