a1=-2,an=54 Find the common difference (d) and sum of the fifteen terms

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Assuming n=15 and a1 is the first term, the series is -2,-2+d,-2+2d, -2+3d,...

a15=54=-2+(15-1)d; 54=-2+14d, 14d=56, d=4.

Series is -2, 2, 6, 10, ..., 54.

Sum of series is 15*(-2)+0+4+8+12+...

Sum=-30+4(1+2+3+...+14)=-30+4(14*15/2)=-30+420=390.
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