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Serhud [2]
3 years ago
7

Factor out the coefficient of the variable 1/2d+6

Mathematics
2 answers:
IrinaK [193]3 years ago
5 0
Factoring out the 1/2 (that is the coefficient of the variable) would require you to divide the equation by one half, which is the same as multiplying by two. After doing this, the answer can be expressed as:

1/2 (d+12)
lyudmila [28]3 years ago
3 0

Answer:

The factor out coefficient of the variable is \frac{1}{2}

Step-by-step explanation:

Given : Expression \frac{1}{2}d+6

To find : Factor out the coefficient of the variable expression ?

Solution :

A coefficient is defined as a number or constant before a variable (with positive or negative sign).

In the expression, \frac{1}{2}d+6

The variable is 'd'.

Taking common constant from both terms to factor out is

\frac{1}{2}d+6=\frac{1}{2}(d+12)

Therefore, The factor out coefficient of the variable is \frac{1}{2}

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Find the sum of 14 + 8 + 2+ ... + ( 274) + (-280).
Musya8 [376]

The sum of the given sequence is -6384.

<u>Step-by-step explanation:</u>

The given Arithmetic sequence is 14 + 8 + 2+ ... + ( 274) + (-280).

  • The first term of the sequence = 14
  • The last term of the sequence = -280
  • The common difference ⇒ 14 - 8 = 6

<u>To find the number of terms in the sequence :</u>

The formula used is n = (\frac{a_{n}-a_{1}} {d})+1

where,

  • n is the number of terms.
  • a_{n} is the late term which is -280.
  • a_{1} is the first term which is 14.
  • d is the common difference which is 6.

Therefore, n =(\frac{-280-14}{6}) +1

⇒ n =( \frac{-294}{6}) + 1

⇒ n = -49 + 1

⇒ n = -48

⇒ n = 48, since n cannot be negative.

∴ The number of terms, n = 48.

<u>To find the sum of the arithmetic progression :</u>

The formula used is S = \frac{n}{2}(a_{1} + a_{n} )

where,

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  • a_{n} is the late term which is -280.

Therefore, S = \frac{48}{2}(14+ (-280))

⇒ S = \frac{48}{2}(-266)

⇒ S = 48 \times -133

⇒ S = -6384

∴ The sum of the given sequence is -6384.

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