Question

How many terms of the A.p 18,16,14 ... be taken so that their sum is zero?​

Answer 1

19 terms

Explanation:

the sum to n terms of an AP is

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 18 and d = a₂ - a₁ = 16 - 18 = - 2, then solving for n

`(n)/(2)` [ (2 × 18) - 2(n - 1) ] = 0 ( multiply both sides by 2 to clear the fraction )

n(36 - 2n + 2) = 0

n(38 - 2n) = 0 ← distribute parenthesis on left side by n

38n - 2n² = 0 ← factor out 2n from each term on the left

2n(19 - n) = 0

equate each factor to zero and solve for n

2n = 0 ⇒ n = 0

19 - n = 0 ⇒ n = 19

n > 0 , then number of terms is 19