a sequence is defined recursively by the formula f(n + 1) = -2f(n). the first term of the sequence is -1.5…
a sequence is defined recursively by the formula f(n + 1) = -2f(n). the first term of the sequence is -1.5. what is the next term in the sequence?\n○ -3.5\n○ -3\n○ 0.5\n○ 3
Answer
Explanation:
Step1: Identify the recursive formula
The recursive formula is ( f(n + 1)=-2f(n) ), and the first term ( f(1)=-1.5 ). We need to find the next term, which is ( f(2) ).
Step2: Substitute ( n = 1 ) into the formula
Substitute ( n = 1 ) into ( f(n + 1)=-2f(n) ), we get ( f(2)=-2\times f(1) ).
Step3: Calculate the value of ( f(2) )
Since ( f(1)=-1.5 ), then ( f(2)=-2\times(-1.5) = 3 ).