The sequence is defined by a recursion formula.Write the first four terms;
a_1=-5; a_n=2a_n-1 +7
a_1 = -5
a_2 = 2(-5)+7 = 3
and so on
To find the first four terms of the sequence defined by the recursion formula a_1 = -5 and a_n = 2a_n-1 + 7, we can use the formula repeatedly to calculate each term sequentially.
Given:
a_1 = -5
a_n = 2a_n-1 + 7
First term (n = 1):
a_1 = -5 (given)
Second term (n = 2):
a_2 = 2a_1 + 7 = 2(-5) + 7 = -10 + 7 = -3
Third term (n = 3):
a_3 = 2a_2 + 7 = 2(-3) + 7 = -6 + 7 = 1
Fourth term (n = 4):
a_4 = 2a_3 + 7 = 2(1) + 7 = 2 + 7 = 9
Therefore, the first four terms of the sequence are:
a_1 = -5
a_2 = -3
a_3 = 1
a_4 = 9