Give the first five terms of the geometric sequence. 𝑎𝑛=−2⋅2^𝑛−1

Answer 1

an = -2(2^n) - 1

a1 =-4-1 = -5

a2 =-9

a3 = -17

a4 =-33

a5 = -65

but interpreting it this way, it's not a geometric sequence, as there is no common ratio 9/5 does not= 17/9

although it's very close to a common ratio of slightly less than 2

so, it must be

an = -2(2^n-1)

a1 =-2(2^0) = -2

a2 = 2(-2) = -4

a3 =2(-4) = -8

a4 =2(-8) = -16

a5 =2(-16) = -32

the common ratio is 2, -4/-2 = -8/4 = -16/-8 = -32/-16 = 2

each term is 2 times the previous term

Answer 2

There is a bit of an issue with how the problem was inputted. The minus 1 can be interpreted to be part of the exponent. For example, is it 2ⁿ - 1 or 2^n-1. If it is the first one, then the previous answer is correct (-5, -9, -17, -33, and -65). If it is like the second one, then the answer is:

a₁ = -2•2^1-1= -2

a₂ = -2•2^2-1= -4

a₃ = -2•2^3-1= -8

a₄ = -2•2^4-1= -16

a₅ = -2•2^5-1= -32