an arithmetic series has first term 160 and common difference d . the sum of the first 25 terms of the series 3500 . find the co
1 answer:
Answer:
d = -
Step-by-step explanation:
The sum to n terms of an arithmetic series is
=
[ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 160, n = 25 and = 3500 , thus
[ (2 × 160) + 24d ] = 3500, that is
12.5(320 + 24d) = 3500 ( divide both sides by 12.5 )
320 + 24d = 280 ( subtract 320 from both sides )
24d = - 40 ( divide both sides by 24 )
d = - = -
You might be interested in
Answer: The correct option is (D) SET 4.
Step-by-step explanation: We are to select the correct set of side lengths that will form a right-angled triangle.
To form a right-angled triangle, we must have the following relation:
<em>Perpendicular² + Base² = Hypotenuse².</em>
<em>Hypotenuse is the length of the largest side; perpendicular and base are the two legs of the triangle.</em>
SET 1 : 14 cm, 5 cm, 6 cm.
We have
Therefore,
<em>Perpendicular² + Base² ≠ Hypotenuse².</em>
So, this set will not form a right-angled triangle.
SET 2 : 8 in., 12 in., 20 in.
We have
Therefore,
<em>Perpendicular² + Base² ≠ Hypotenuse².</em>
So, this set will not form a right-angled triangle.
SET 3 : 10 mm, 20 mm, 30 mm.
We have
Therefore,
<em>Perpendicular² + Base² ≠ Hypotenuse².</em>
So, this set will not form a right-angled triangle.
SET 4 : 12 ft, 16 ft, 20 ft.
We have
Therefore,
<em>Perpendicular² + Base² = Hypotenuse².</em>
So, this set will form a right-angled triangle.
Thus, the SET 4 will form a right-angles triangle.
Option (D) is correct.