The nth term of a a geometric sequence is given by a_n=27(0.1)^n-1 . Write the first five terms of this sequence.
Can i get some help
n= the number in the sequence
for the first term plug in 1 for n
for the second 2 for n
and so on.
start with the 1st term (recall that x^0 = 1)
Then to get each next term, just keep multiplying by 0.1
Of course! I can help you with that.
To find the first five terms of a geometric sequence, we need to substitute different values of 'n' into the given formula, which is:
aₙ = 27(0.1)^(n-1)
Let's substitute values for n from 1 to 5 and calculate each term:
To find the first term (a₁), substitute n = 1 into the formula:
a₁ = 27(0.1)^(1-1)
a₁ = 27(0.1)^0
a₁ = 27(1)
a₁ = 27
So, the first term of the sequence is 27.
Similarly, we can find the subsequent terms:
To find the second term (a₂), substitute n = 2:
a₂ = 27(0.1)^(2-1)
a₂ = 27(0.1)^1
a₂ = 27(0.1)
a₂ = 2.7
The second term of the sequence is 2.7.
To find the third term (a₃), substitute n = 3:
a₃ = 27(0.1)^(3-1)
a₃ = 27(0.1)^2
a₃ = 27(0.01)
a₃ = 0.27
The third term of the sequence is 0.27.
To find the fourth term (a₄), substitute n = 4:
a₄ = 27(0.1)^(4-1)
a₄ = 27(0.1)^3
a₄ = 27(0.001)
a₄ = 0.027
The fourth term of the sequence is 0.027.
Finally, to find the fifth term (a₅), substitute n = 5:
a₅ = 27(0.1)^(5-1)
a₅ = 27(0.1)^4
a₅ = 27(0.0001)
a₅ = 0.0027
The fifth term of the sequence is 0.0027.
Therefore, the first five terms of the given geometric sequence are:
27, 2.7, 0.27, 0.027, 0.0027.