How to read it all in a sentence Step 1: Identify the first term (a1a1​)

The first term of the sequence is given as 1661​.

Step 2: Determine the common difference (dd)

The common difference dd is found by subtracting the first term from the second term. For this sequence:

d=13−16=26−16=16d=31​−61​=62​−61​=61​

Verify by subtracting the second term from the third term:

12−13=36−26=1621​−31​=63​−62​=61​

So, d=16d=61​.

Step 3: Use the formula for the nth term

The formula for the nnth term of an arithmetic sequence is:

an=a1+(n−1)×dan​=a1​+(n−1)×d

Here, we want to find the 5th term (a5a5​).

Step 4: Substitute the values

Substitute a1=16a1​=61​, d=16d=61​, and n=5n=5 into the formula:

a5=16+(5−1)×16a5​=61​+(5−1)×61​a5=16+4×16a5​=61​+4×61​a5=16+46=1+46=56a5​=61​+64​=61+4​=65​

Step 5: Conclude the answer

The 5th term of the sequence is 5665​.