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Answer: 148

    110 + 111 + 112 + 113 + 114 + 115 + 116 + 117 + 118
or 120 + ... + 128
     etc
sum = 9$\times$ middle number
114$\times$9
124$\times$9
134$\times$9
144$\times$9 = 12$^2\times$3$^2$ = (12$\times$3)$^2$ so is a square number

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.