If an and bn equal the following find a7 b7 an 1 2 4 8 bn

If {a_n} and {b_n} equal the following, find a_7 + b_7. {a_n{ = -1, 2, -4, 8, ..., {b_n} = 5, -4, -13, -22, ..., a_7 + b_7 =

Solution

{a_n} is gemetric sequence with r=-2, a=-1

Hence general term = ar^n-1 = a_n

For n=7, a₇ = -1(-2)^7-1 = -(-2)⁶ = -64

a₇ = -64

Now {b_n} is geometric sequence with common difference d = -4-5 = -9, a=5

The general term here is b_n = a+(n-1)d

For n=7, b₇ = 5+(7-1)(-9) = 5-54 = -49

Hence a₇ + b₇ = -64-49 = -113