The ratio of 11th term to the 18th term of an AP is 2: 3. Find the ratio of the 5th term to the 21st terms.
And also the ratio of the sum of the first five terms to the sum of first 21 terms.
Answers
Answered by
29
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
Answered by
20
answer is in attachment
hope it helps you
please mark as brainliest
Attachments:
Similar questions