Question

A-59 Trixie wants to create an especially tricky arithmetic sequence. She wants the 5th term of the sequence to equal 11 and the 50th term to equal 371. That is, she wants t(5)=11 and t(50)=371. Is it possible to create an arithmetic sequence to fit her information?

Answer 1

Yes, it is possible for Trixie to create an arithmetic sequence with t(5)=11 and t(50)=371, by using the formula for an arithmetic sequence and the provided information to find the first term and the common difference.

The sequence will have a first term of -21 and a common difference of 8.

Step-by-step explanation:

To determine if it's possible for Trixie to create an arithmetic sequence where t(5)=11 and t(50)=371, we need to use the formula for an arithmetic sequence:

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

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

From the given information, we can create two equations:

1. a + 4d = 11 (for the 5th term)
2. a + 49d = 371 (for the 50th term)

Subtracting equation 1 from equation 2 to eliminate a:

45d = 360

Diving both sides by 45:

d = 8

Using d = 8 in equation 1, we can solve for a:

a + 4(8) = 11

a + 32 = 11

a = -21

Therefore, the common difference, d, is 8 and the first term, a, is -21.

An arithmetic sequence with these values is possible, and Trixie can create the desired sequence.