Answer: 93

Small Hint:

Pair the odd-indexed terms with the even-indexed terms

Big Hint:

Each even-indexed term is $1$ greater than the odd-indexed term immediately before it

Solution:

Let $E=a_2+a_4+\cdots+a_{98}$ and $O=a_1+a_3+\cdots+a_{97}.$ There are $49$ pairs, and $a_{2k}-a_{2k-1}=1,$ so $E-O=49.$ Also $E+O=137.$ Adding the two equations gives $2E=186,$ and hence $E=93.$