— A friend of mine.

A Policeman and a Thief  
One day a policeman was taking a thief to the city . On the way , they saw a shop . The thief said . “ Let me go into the shop to buy some bread . We can eat it in the train . ”
The policeman agreed . The thief went into the shop and ran out of the back door . When the policeman knew that , he began to look for the thief everywhere . At last the policeman caught(抓获) thief again . They went on to the city . On the way they came to the same shop . The thief wanted to buy some bread again . “Oh , no . ” said the policeman , “You did that before , and you ran away . This time I^’ll go into the shop and buy bread . You must wait here for me . ”

设$s_n$为等差数列$\left\{a_n\right\}$的前n项和，若$a_1=1$，公差d=2，  $s_{k+2}-s_k=24$，则k=(    )