Find the first five terms of each sequence.
a^n = 2a^n- 1 - 1, where a1 = 2
they specifically said, "a1 = 2"
so the calculations are
a2 = 2a1-1 = 2*2-1 = 3
a3 = 2a2-1 = 2*3-1 = 5
a4 = 2a3-1 = 2*5-1 = 9
a5 = 2a4-1 = 2*9-1 = 17
so the sequence is 2,3,5,9,17,
Apologies for the oversight. You are correct. When a1 = 2, the first five terms of the sequence are:
2, 3, 5, 9, 17. Thank you for pointing that out.
To find the first five terms of the sequence defined by a^n = 2a^n-1 - 1, where a1 = 2, we can start by plugging in the values of n from 1 to 5.
1. When n = 1:
a^1 = 2a^0 - 1
a = 2(1) - 1
a = 2 - 1
a = 1
2. When n = 2:
a^2 = 2a^1 - 1
a^2 = 2(1) - 1
a^2 = 2 - 1
a^2 = 1
3. When n = 3:
a^3 = 2a^2 - 1
a^3 = 2(1) - 1
a^3 = 2 - 1
a^3 = 1
4. When n = 4:
a^4 = 2a^3 - 1
a^4 = 2(1) - 1
a^4 = 2 - 1
a^4 = 1
5. When n = 5:
a^5 = 2a^4 - 1
a^5 = 2(1) - 1
a^5 = 2 - 1
a^5 = 1
Therefore, the first five terms of the sequence are:
1, 1, 1, 1, 1