A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.
an =
an − 1
3
and a1 = −12
a1 =
a2 =
a3 =
a4 =
a5 =
To find the first five terms of the sequence, we can use the recursive formula.
Given that a1 = -12, we can find a2 by substituting n = 2 into the formula:
a2 = (a2-1)/3 = (-12)/3 = -4
Similarly, we can find a3 by substituting n = 3:
a3 = (a3-1)/3 = (-4)/3 = -4/3
Continuing this pattern, we can find a4 and a5:
a4 = (a4-1)/3 = (-4/3)/3 = -4/9
a5 = (a5-1)/3 = (-4/9)/3 = -4/27
Therefore, the first five terms of the sequence are:
a1 = -12
a2 = -4
a3 = -4/3
a4 = -4/9
a5 = -4/27
To find the first five terms of the sequence defined recursively by the given formulas, we can substitute the values of n into the formula and calculate each term step by step.
Given:
a_n = a_{n-1}/3
a_1 = -12
Substituting n=1 into the formula:
a_1 = a_{1-1}/3
a_1 = a_0/3
Since a_1 is given as -12, we can substitute it into the equation:
-12 = a_0/3
To find a_0, we can solve for it by multiplying both sides of the equation by 3:
-12 * 3 = a_0
-36 = a_0
Now, we can calculate the first five terms of the sequence:
a_1 = -12
a_2 = (-12)/3 = -4
a_3 = (-4)/3 = -4/3
a_4 = (-4/3)/3 = -4/9
a_5 = (-4/9)/3 = -4/27
Therefore, the first five terms of the sequence are:
a_1 = -12
a_2 = -4
a_3 = -4/3
a_4 = -4/9
a_5 = -4/27