Multiple choice

$a, 2a -1, 3a -2, 4a -3, . . .$ For a particular number $a$, the first term in the sequence above is equal to $a$ and each term thereafter is $7$ greater than the previous term. What is the value of the $16th$ term in the sequence?

  1. $113$
  2. $110$
  3. $96$
  4. $120$
  5. $130$
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A Correct answer
Explanation

The sequence is an arithmetic progression with first term a and common difference 7. The 16th term is a + (16-1)*7 = a + 105. The first term is a, second is 2a-1. So 2a-1 = a+7, which means a=8. The 16th term is 8 + 105 = 113.

AI explanation

The sequence is defined as an arithmetic progression because each term is 7 greater than the previous one, making the first term a and the common difference 7. Using the arithmetic sequence formula, the nth term is calculated as a + (n-1)d. Substituting n = 16 and d = 7 gives the result a + (16-1)7, which simplifies to a + 105. Since the first term a is 8 (from the difference between a and 2a-1 being 7), the 16th term is 8 + 105 = 113.

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