Question

The first two terms of a sequence are a1 =4 and a2= -2. Let a3 be the third term when the sequence is arithmetic and let b3 be the third term when the sequence is geometric. Find a3+b3

Answer 1

a3 + b3 = -7

Explanation:

When the sequence is A.P

a1 =4 and a2= -2

Common difference,d = a2 - a1

= -2 - 4

d = -6

a3 = third term

a3 = a1 + 2d

= 4 + 2(-6)

= 4 - 12

= -8

a3 = -8

When the sequence is geometric

a1 =4 and a2= -2

Common ratio, r = a2/a1

= -2/4

r = -1/2

Or

r = -0.5

b3 = third term

b3 = ar²

= 4 * (-1/2)²

= 4 * 1/4

= 4/4

= 1

b3 = 1

a3 + b3 = -8 + 1

= -7

a3 + b3 = -7