Let a is the first term and d is the common difference of the AP

Given 8th term of an A.P = 15

=> a + (8-1)d = 15

=> a + 7d = 15 ..............1

Now,

Sum of 15 terms S₁₅ = (15/2)*{2a + (15-1)d}

=> S₁₅ = (15/2)*{2a + 14d}

=> S₁₅ = 15*{a + 7d}

=> S₁₅ = 15*15         {from equation 1}

=> S₁₅ = 225