The sequence is defined by a recursion formula, write the first four terms of the sequence;
a_1=100; a_n=1/2a_n-1 +4
Did you bother to even attempt to solve any of you questions. How about you show some of your work and we can go from there.
And that was a statement, not a question.
To find the first four terms of the given sequence defined by a recursion formula, we will use the formula recursively.
Given: a_1 = 100 and a_n = (1/2)a_(n-1) + 4.
Let's start with the first term:
a_1 = 100 (already given).
Now, we can use the recursive formula to find the remaining terms:
For the second term:
a_2 = (1/2)a_1 + 4
= (1/2)(100) + 4
= 50 + 4
= 54
For the third term:
a_3 = (1/2)a_2 + 4
= (1/2)(54) + 4
= 27 + 4
= 31
For the fourth term:
a_4 = (1/2)a_3 + 4
= (1/2)(31) + 4
= 15.5 + 4
= 19.5
Therefore, the first four terms of the sequence are: 100, 54, 31, 19.5.