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Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

A(n) = 1 + (n – 1)(–4.1)

1, –11.3, –35.9

0, –12.3, –36.9

–4.1, –15.4, –36.9

1, –15.4, –40

1 answer

To find the first, fourth, and tenth terms of the arithmetic sequence described by the formula \( A(n) = 1 + (n - 1)(-4.1) \), we can substitute \( n = 1 \), \( n = 4 \), and \( n = 10 \) into the formula.

  1. First term \( A(1) \): \[ A(1) = 1 + (1 - 1)(-4.1) = 1 + 0 = 1 \]

  2. Fourth term \( A(4) \): \[ A(4) = 1 + (4 - 1)(-4.1) = 1 + 3(-4.1) = 1 - 12.3 = -11.3 \]

  3. Tenth term \( A(10) \): \[ A(10) = 1 + (10 - 1)(-4.1) = 1 + 9(-4.1) = 1 - 36.9 = -35.9 \]

Thus, the first, fourth, and tenth terms are:

  • First term: \( 1 \)
  • Fourth term: \( -11.3 \)
  • Tenth term: \( -35.9 \)

The correct sequence of terms is \( 1, -11.3, -35.9 \), which corresponds to the first option.