Question

The third term of an arithmetic sequence is 18.6 And the fifth term is 29.2. Determine the nᵗʰ term of the sequence

Answer 1

To determine the nᵗʰ term of an arithmetic sequence, we calculate the common difference and the first term using the given terms. The common difference is found to be 5.3, and the first term is 8. Therefore, the formula for the nᵗʰ term is an = 8 + (n - 1)(5.3).

Step-by-step explanation:

To find the nᵗʰ term of an arithmetic sequence, first, we need to determine the common difference (d). We’re given that the third term (a3) is 18.6, and the fifth term (a5) is 29.2.

We can set up the following equations from the definition of an arithmetic sequence:

• 
  
• a3 = a1 + 2d = 18.6,
• 
  
• a5 = a1 + 4d = 29.2.

By subtracting the first equation from the second equation, we get:

1. 
   
3. 29.2 - 18.6 = (a1 + 4d) - (a1 + 2d),
4. 
   
6. 10.6 = 2d,
7. 
   
9. d = 5.3.

Now, we can find a1 by substituting d back into one of the original equations:

1. 
   
3. 18.6 = a1 + 2(5.3),
4. 
   
6. 18.6 = a1 + 10.6,
7. 
   
9. a1 = 8.

The general formula for the nᵗʰ term (an) of an arithmetic sequence is:

an = a1 + (n - 1)d.

Thus, the nᵗʰ term is:

an = 8 + (n - 1)(5.3).