Question

In the first term of an AP is 3 the sum of first 5 terms is 1/11th of the sum of next 5 terms. Find the 20th term

Answer 1

Answer:

-35

Step-by-step explanation:

Generally AP is denoted as a + (a + d) + (a + 2d) + (a + 3d) + .... + (a + nd).

Given that the  first term of AP is 3 i.e. a = 3, so the AP becomes

3 + (3 + d) + (3 + 2d) + (3 + 3d) + .... + (3 + nd).

Given that sum of first five terms = $\frac{1}{11}$ of sum of next 5 terms

⇒ 3 + (3 + d) + (3 + 2d) + (3 + 3d) + (3 + 4d) = $\frac{1}{11}$ (3 + 5d) + (3 + 6d) + (3 + 7d) + (3 + 8d) + (3 + 9d

⇒ 15 + 10d = $\frac{1}{11}$ (15 + 35d)

⇒ (15 + 10d) × 11 = 15 + 35d

⇒ 165 + 110d = 15 + 35d

⇒ 110d - 35d = 15 - 165

⇒ 75d = -150

⇒d = ${-150}{75}$ = -2

Now we have d = -2. So the 20th term of the AP would be 3 + 19d

⇒ 3 + 19 × (-2) = 3 + -38 = -35

∴ The 20th term of the AP is - 35.