Question

The first two terms of an arithmetic progression are 27 and 24 respectively. How many terms of the progression are to be added to get - 30?

Answer 1

20 terms

Explanation:

Given AP with the first two terms:

• a₁= 27 and a₂=24

Common difference:

• d= 24-27 = -3

To find

• n for which Sₙ= -30

Solution

• Sₙ = 1/2*n*(a₁+aₙ) =
• 1/2n(a₁+a₁+(n-1)d) =
• 1/2n(27+27+(n-1)(-3))=
• 1/2n(54 - 3n + 3) =
• 1/2n(57 - 3n)

Since Sₙ = -30

• 1/2n(57 - 3n) = -30
• 57n - 3n² = -60
• 19n - n²- 20 = 0
• n² -19 n -20= 0

Solving the quadratic equation we get:

• n =20

So the sum of 20 terms will add up - 30