If the ratio of the 11th term of an AP to its 18th term is 2:3 find the ratio of the sum of the fust five term to the sum of its first 10 term?
Answers
As we got that the RATIO OF THE 11TH TERM WITH 18TH TERM as.
Let the First term and Common Difference be A and D Respectively.
- T₁₁ = A + 10D
- T₁₈ = A + 17D
→ [A + 10D]/[A + 17D] = 2/3
→ 3[A + 10D] = 2[A + 17D]
→ 3A + 30D = 2A + 34D
→ A = 4D ...[1]
Now, I am going to Find the RATIO of the sum of first five terms to the sum of its first ten terms.
→ S₅ = 5/2[2A + (5-1)D]
→ S₅ = 5/2[ 2×4D + (4)D]
→ S₅ = 5/2 [8D + 4D]
→ S₅ = 5[4D + 2D]
→ S₅ = 5[6D]
→ S₅ = 30D
→ S₁₀ = 10/2[2A + (10-1)D]
→ S₁₀ = 10/2[ 2×4D + (9)D]
→ S₁₀ = 5 [8D + 9D]
→ S₁₀ = 5[8D + 9D]
→ S₁₀ = 5[17D]
→ S₁₀ = 65D
Finally, It's time to compare S₅ and S₁₀ to form RATIO as.
- → 30D/65D = 6/17 = 6 : 7