Possible explanation:

The given series alternates between two patterns: a palindrome (a word or phrase that reads the same backward as forward) and its reverse, with some additional letters or symbols inserted in between. To complete the series, we need to follow this pattern and find the next palindrome with an added letter or symbol, then reverse it and add another letter or symbol, and so on, until we reach the last letter "b".

ab____d___aaba___na____badna___ b

1. First palindrome: abba
We can add two identical letters, one at each end, to form a four-letter palindrome.

abba

2. Reverse and add: adbd
We can reverse the previous palindrome and add two different letters, one at each end.

abba - adbd

3. Palindrome with repetition: aaba
We can repeat the first two letters and add two more letters in between to form a new palindrome.

abba - adbd - aaba

4. Reverse and add: ana
We can reverse the previous palindrome and add two letters that form a word (meaning "of each kind" in Sanskrit).

abba - adbd - aaba - ana

5. Palindrome with insertion: badna
We can insert the previous palindrome in between two letters, one being the same as the first letter and the other being the same as the last letter, to form a new palindrome.

abba - adbd - aaba - ana - badna

6. Reverse and add: andaa
We can reverse the previous palindrome and add two letters that form a word (meaning "egg" in Tamil).

abba - adbd - aaba - ana - badna - andaa - b

Therefore, the next term in the series is "andaa".