Final answer:
To find the n-th term of an arithmetic sequence, we can use the formula aₙ = a₁ + (n - 1)d, where a₁ is the first term, d is the common difference, and n represents the position of the term we want to find.
Step-by-step explanation:
To find the nᵗʰ term of an arithmetic sequence, we first need to find the common difference in the sequence. The common difference is the difference between any two consecutive terms in the sequence. In this case, the third term is 8 and the fifth term is 26. So, the common difference is obtained by subtracting the third term from the fifth term: 26 - 8 = 18.
Now that we know the common difference is 18, we can find the nᵗʰ term using the formula:
aₙ = a₁ + (n - 1)d
where a₁ is the first term, d is the common difference, and n represents the position of the term we want to find.
Since we don't know the first term, we'll extract it by substituting the values we have so far:
a₃ = a₁ + (3 - 1) * 18 = a₁ + 36
We know that a₃ is 8, so we can set up the equation:
8 = a₁ + 36
Now, isolate a₁:
a₁ = 8 - 36
a₁ = -28
Now that we have the first term, we can use the formula to find the nᵗʰ term:
aₙ = -28 + (n - 1) * 18