the ratio of the 11th term to the 18th term of an ap is 2:3 find the ratio of the 5th term 21st and also the ratio of the sum of the first 5th term of the first 21st term
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Answer:
a₁₁ / a₁₈ = 2/3
⇒ a+10d / a+17d = 2/3
3(a+10d) = 2(a+17d)
3a + 30d = 2a + 34d
3a - 2a + 30d - 34d = 0
a - 4d = 0
∴ a = 4d
a₅ / a₂₀ = a+4d / a+20d
= 4d+4d / 4d+20d
= 8d / 24d
= 1/3
∴ Ratio of a₅ : a₂₁ = 1 : 3
S₅ / S₂₁ = [5/2 (2a + (5-1)d)] / [21/2 (2a + (21-1)d)]
= [5(2a + 4d)] / [21(2a + 20d)]
= [10a + 20d] / [42a + 420d]
= [10(4d) + 20d] / [42(4d) + 420d]
= 60d / 588d
= 5 / 49
∴ Ratio of S₅ : S₂₁ = 5 : 49
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The ratio of the 11th term of the 18th term of an AP is 2:3. Find the ratio of the 5th term to the 21st term and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
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