The sequence A_n is such that an = 2a_n-1 + 1. If a_6 = 191 and a_5 = 95, what is the
value of a_2?
To find the value of a_2, we can apply the recursive relationship given for the sequence.
We are given that a_5 = 95, so we can use the recursive relationship to find a_6:
a_6 = 2a_5 + 1
a_6 = 2(95) + 1
a_6 = 190 + 1
a_6 = 191
Since we are also given that a_6 = 191, we can substitute this value into the recursive relationship to find a_5:
a_6 = 2a_5 + 1
191 = 2a_5 + 1
190 = 2a_5
a_5 = 95
Now we can continue using the recursive relationship to find a_4:
a_5 = 2a_4 + 1
95 = 2a_4 + 1
94 = 2a_4
a_4 = 47
Continuing in this manner, we find:
a_3 = 2a_2 + 1
a_2 = (a_3 - 1) / 2
a_2 = ((2a_4 + 1) - 1) / 2
a_2 = (2a_4) / 2
a_2 = a_4
a_2 = 47
Therefore, the value of a_2 is 47.