4. In the sequence $\left\{a_{n}\right\}$, $a_{k}+a_{k+1}=2 k+1\left(k \in \mathbf{N}^{*}\right)$, then $a_{1}+a_{100}$ equals
4. 101 Detailed Explanation: $a_{1}+a_{100}=\sum_{k=1}^{99}\left(a_{k}+a_{k+1}\right)(-1)^{k-1}=\sum_{k=1}^{99}(2 k+1)(-1)^{k-1}=(3-5)+(7-9)+\cdots$ $+199=-2 \times 49+199=101$