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The first 4 numbers of an arithmetic sequence are given below: 16, 12, 8, 4. What is the value of the 150th term of the sequence?

A) -596
B) 596
C) 604
D) -604

User Aariba
by
8.9k points

1 Answer

3 votes

Final answer:

The 150th term of the arithmetic sequence (16, 12, 8, 4) with a common difference of -4 is -580, which is calculated using the nth term formula for an arithmetic sequence.

Step-by-step explanation:

The first 4 numbers of an arithmetic sequence are given: 16, 12, 8, 4. In an arithmetic sequence, each term is equal to the previous term plus a constant difference. In this case, the difference is -4 (since 12 - 16 = -4, 8 - 12 = -4, and so on).

To find the value of the 150th term of the sequence, we use the formula for the nth term of an arithmetic sequence:

Tn = a + (n - 1)d, where:

  • Tn is the nth term of the sequence,
  • a is the first term of the sequence,
  • n is the term number,
  • d is the common difference.

Plugging in the given values:

T150 = 16 + (150 - 1)(-4)

T150 = 16 + (149)(-4)

T150 = 16 - 596

T150 = -580

Therefore, the value of the 150th term of the sequence is -580, which is not listed in the options provided. It seems there might be an error in the provided choices.

User TomSlick
by
8.1k points
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