Question

The third term of an arithmetic sequence is 137 And the fifth term is 257. Determine the nᵗʰ term of the sequence

Answer 1

To determine the nʹ term of the arithmetic sequence where the third term is 137 and the fifth term is 257, first calculate the common difference, then find the first term and use the arithmetic sequence formula.

Step-by-step explanation:

To find the nʹ term of an arithmetic sequence, we can use the formula for any term of an arithmetic sequence which is a_n = a_1 + (n-1)d, where a_n is the nʹ term, a_1 is the first term, and d is the common difference. Given that the third term is 137 and the fifth term is 257, we can set up the following equations:

• a_1 + 2d = 137
• a_1 + 4d = 257

Subtracting the first equation from the second gives us:

• 2d = 120

Solving for d gives us d = 60. Using this common difference and the third-term value, we can find the first term:

• a_1 = 137 - 2(60) = 17

Now, with a_1 and d known, the formula for the nʹ term is:

• a_n = 17 + (n-1)(60)

This equation will give us the nʹ term of the arithmetic sequence when we plug in any positive integer for n.