30.8k views
3 votes
Write an explicit formula for the sequence {an} = {-3, -(1/2), 2, (9/2), 7, ...}. then, find a17.

1 Answer

2 votes

Final answer:

The explicit formula for the sequence is an = -3 + (n-1) × (5/2). Using this formula, we find that the 17th term, a17, is 37.

Step-by-step explanation:

To write an explicit formula for the sequence {an} = {-3, -(1/2), 2, (9/2), 7, ...}, we first observe the pattern of the sequence. We can see that each term is obtained by adding 5/2 to the previous term. Since the first term a1 is -3, we can develop the formula an = -3 + (n-1) × (5/2).

To find a17, we substitute 17 for n in the formula:

a17 = -3 + (17-1) × (5/2)
a17 = -3 + 16 × (5/2)
a17 = -3 + 40
a17 = 37.

Hence, the 17th term of the sequence is 37.

User Sergei Golos
by
8.4k points