Question

The third term of an arithmetic sequence is 26 And the fifth term is 40. Determine the nᵗʰ term of the sequence

Answer 1

To find the nᵗʰ term of an arithmetic sequence with the third term 26 and the fifth term 40, we calculate the common difference to be 7 and the first term to be 12. Using these values, the nᵗʰ term is given by the formula aₙ = 12 + 7(n - 1).

Step-by-step explanation:

To determine the nth term of an arithmetic sequence when given the third and fifth terms, we first need to find the common difference (d) and the first term (a1). We know that the third term, a3, is 26 and the fifth term, a5, is 40. Using the formula for the nth term of an arithmetic sequence, an = a1 + (n - 1)d, we can set up a system of two equations:

• a3 = a1 + 2d = 26
• a5 = a1 + 4d = 40

Subtracting the first equation from the second gives us:

• 2d = 14

Therefore, d = 7.

Substituting d = 7 into the first equation, we get:

• a1 + 14 = 26

So, a1 = 12.

Now we know that the first term is 12 and the common difference is 7. The nth term formula becomes:

• an = 12 + (n - 1) * 7

Therefore, the nth term of the arithmetic sequence is an = 12 + 7(n - 1).

Answer 2

Fourth term = (26 + 40)/2 = 66/2 = 33

So the common difference is 7.

Second term = 26 - 7 = 19

First term = 19 - 7 = 12

a(n) = 12 + 7(n - 1)