Question

If x, |x + 1, \X – 1| are the
three terms of an A.P its
sum upto 20 terms is

Answer 1

Answer:

180

Step-by-step explanation:

Answer 2

The sum up to 20 terms is 105

Given:

x, |x + 1| are |x - 1| in A.P

Step-by-step explanation:

2b = a + c ⇒ 2|x + 1| = x + |x - 1|

If |x < 1| ⇒ 2(1 - x) = -x - x - 1 ⇒ 2 = -1 ⇒ no solutions.

If |-1 ≤ x ≤ 0| ⇒ 2(1 - x) = -x + x + 1 ⇒ x = 1/2 ⇒ solution is not in the interval [-1, 0].

If |0 < x ≤ 1| ⇒ 2(1 - x) = x + x + 1 ⇒ x = 1/4 ⇒ one solution.

If |x > 1| ⇒ 2(x - 1) = x + x + 1 ⇒ -2 = 1 ⇒ no solution.

Thus, the only solution of the formed equation is x = 1/4.

On substituting value of 'x' in given terms, we get, 1/4, 3/4 and 5/4

The common difference is 1/2

The 20th term of the given series is given by the formula:

1/4 + ((1/2) × 20) = 1/4 + 10 = 41/4

The sum of the first 20th term is given as:

S₂₀ = ((1/2)(1/4 + 41/4)) × 20 = 105