Answer:
Sum of the first 15 terms = -405
Explanation:
a + 3d = -15 (1)
a + 8d = -30 (2)
Where,
a = first term
d = common difference
n = number of terms
Subtract (1) from (1)
8d - 3d = -30 - (-15)
5d = -30 + 15
5d = -15
d = -15/5
= -3
d = -3
Substitute d = -3 into (1)
a + 3d = -15
a + 3(-3) = -15
a - 9 = -15
a = -15 + 9
a = -6
Sum of the first 15 terms
S = n/2[2a + (n − 1) × d]
= 15/2 {2×-6 + (15-1)-3}
= 7.5{-12 + (14)-3}
= 7.5{ -12 - 42}
= 7.5{-54}
= -405
Sum of the first 15 terms = -405