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Difficulty: EasyArithmetic and Geometric Sequences and Series

The first term of an arithmetic sequence is 88, and the second term is 55. What is the 66 th term of this sequence?

  1. A
    -15
  2. B
    -10
  3. -7Answer
  4. D
    -4
  5. E
    23

Answer

-7
The correct answer is −7-7. Since the sequence is arithmetic, it changes by a constant common difference, dd, with each step. Calculating dd gives 5−8=−35 - 8 = -3. To find the 66 th term, we start at the first term, 88, and add the common difference 55 times (representing the steps from the first to the sixth term): 8+5(−3)=8−15=−78 + 5(-3) = 8 - 15 = -7.

Step-by-Step Solution

1
Determine the common difference, dd, of the arithmetic sequence.
d=−3d = -3
Subtract the first term from the second term: 5−8=−35 - 8 = -3.
2
Set up the equation for the nn th term of an arithmetic sequence, an=a1+(n−1)da_n = a_1 + (n-1)d.
a6=8+(6−1)(−3)a_6 = 8 + (6-1)(-3)
We want to find the 6th term (n=6n = 6) starting with a1=8a_1 = 8 and d=−3d = -3.
3
Perform the operations to find the final value.
a6=−7a_6 = -7
First multiply 5×(−3)=−155 \times (-3) = -15, then add to 88 to get 8−15=−78 - 15 = -7.

Key Concept

Finding a specific term of an arithmetic sequence using its first term and common difference.
Estimated Time:45s
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Topics

Arithmetic and Geometric Sequences and Series

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