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3 years ago

What is the equation of an arithmetic sequence with a first term of 6 and a second term of 2?

Mathematics

1 answer:

kifflom [539]3 years ago

3 0

Answer:

The equation of the sequence = 10 - 4n

Step-by-step explanation:

The rule of the arithmetic sequence is Tn = a + (n - 1)d

Where a is the first term , d is the difference between each consecutive terms and n is the position of the number in the sequence

∵ First term = 6

∵ Second term = 2

∴ The difference between the second and the first = 2 - 6 = -4

∴ Tn = 6 + (n - 1)(-4) = 6 - 4n + 4 = 10 - 4n

∴ The equation of the sequence = 10 - 4n

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Find an exact value. Cos 75° negative square root of six plus square root of two quantity square root of six minus square root o

ehidna [41]

Answer:

√2(√3 - 1)/4

Step-by-step explanation:

To find an exact value for Cos75°, we use the compound angle formula. Since 75° = 45° + 30°, Cos75° = Cos(45° + 30°).

Using Cos(A + B) = CosACosB - SinASinB where A = 45° and B = 30°,

Cos75° = Cos(45° + 30°) = Cos45°Cos30° - Sin45°Sin30°

Now Cos45° = Sin45° = 1/√2 = √2/2, Cos30° = √3/2 and Sin30° = 1/2.

Substituting these values into the above equation, we have

Cos75° = Cos(45° + 30°)

= Cos45°Cos30° - Sin45°Sin30°

= √2/2 × √3/2 - √2/2 × 1/2

= √6/4 -√2/4

= √2(√3 - 1)/4

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3 years ago

Tan30°+cos30°÷tan30°×cos30°

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Answer:

{1/√3+1/2} ÷{1/√3× 1/2}

(2+√3)/2√3÷(1/2√3)
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(2+1 )+√3 /2√3
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3 years ago