Answer:
The 3rd term is 11
Step-by-step explanation:
The given parameters for the Arithmetic Progression, AP, are;
The ratio of the 7th term to the 10th term = (a + 6·d)/(a + 9·d) = -1
The 16th term = -15 = a + 15·d
The 3rd term= a + 2·d
From the 7th to the 10th term ratio, we have;
a + 6·d = -a - 9·d
2·a = -15·d
-2·a = 15·d...(1)
From the 16th term of the AP, we have;
-15 = a + 15·d = a + -2·a = -a
a = 15
From equation (1), -2·a = 15·d, we have;
-2·a = -2 × 15 = 15·d
15·d = -2 × 15
d = -2 × 15/15 = -2
d = -2
The 3rd term = a + 2·d = 15 + 2 × -2 = 11
∴ The 3rd term = 11
