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2 years ago

Find the sum of the first 50 terms of the sequence -6, -2, 2, 6

Mathematics

1 answer:

monitta2 years ago

4 0

Answer:

4600

Step-by-step explanation:

STEP 1: Determine type of progression

$d1 = - 2 - ( - 6) \\ d1 = 4 \\ \\ d2 = 2 - ( - 2) \\ d2 = 4$

Since d1 = d2, it is Arithmetic progression, with a common difference of 4

STEP 2: Evaluate the sum

$s = \frac{n}{2} (2a + (n - 1)d) \\ s = \frac{50}{2} (2( - 6) + (50 - 1)4) \\ s = 4600$

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Theorem 1: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

Theorem 2: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

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12. South-east point from the previous: By the 2nd theorem,

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