Question

The third term of an arithmetic sequence is 191 And the fifth term is 391. Determine the nᵗʰ term of the sequence

Answer 1

To find the nᵗʰ term of the arithmetic sequence, calculate the common difference from the given terms and use it to establish the sequence formula. The nᵗʰ term is 100n - 109.

Step-by-step explanation:

To find the nᵗʰ term of an arithmetic sequence when given the third term (191) and the fifth term (391), we first need to find the common difference, d. The difference between the third and fifth terms is:

391 - 191 = 200

Since there is one term between the third and fifth terms, we divide the difference by 2 to find the common difference:

d = 200 / 2 = 100

The arithmetic sequence formula for the nᵗʰ term is:

aₙ = a₁ + (n - 1)d

To find the first term (a₁), we use the third term and work backwards:

191 = a₁ + 2(100)

a₁ = 191 - 200

a₁ = -9

Now we can write the formula for the nᵗʰ term of this sequence:

aₙ = -9 + (n - 1)(100)

Or simplified:

aₙ = 100n - 109