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2 years ago

14

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

o get - 30?

1 answer:

Thepotemich [5.8K]2 years ago

4 0

Answer:

20 terms

Step-by-step explanation:

<u>Given AP with the first two terms:</u>

a₁= 27 and a₂=24

<u>Common difference: </u>

d= 24-27 = -3

<u>To find </u>

n for which Sₙ= -30

<h3>Solution</h3>

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)

<u>Since Sₙ = -30</u>

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

<u>Solving the quadratic equation we get:</u>

n =20

So the sum of 20 terms will add up - 30

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