Answer:
a) x = -1.5
b) x = 1
Step-by-step explanation:
For problem a, you can start by subtracting 3x from both sides to gather all the like terms together:
7x + 5 = 3x - 1
-3x -3x
4x + 5 = -1
Next, to get the coefficients on one side, you subtract 5 from both sides:
4x + 5 = -1
-5 -5
4x = -6
Now, you divide by 4 on both sides to isolate x:
x = -6/4 = -1.5 --- > x = -1.5
For problem b, you start by subtracting 3x from both sides(kinda like problem a):
5x + 12 = 3x + 14
-3x -3x
2x + 12 = 14
Next, you can subtract 12 from both sides, isolating the "x term".
2x + 12 = 14
-12 -12
2x = 2
Lastly, you can divide by 2 to get x:
x = 1
Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}
iren [92.7K]
Answer:
A) a_n = 5n + 2
B) a_n = (2^(n + 1)) - 1
Step-by-step explanation:
A) The sequence is given as;
{7,12,17,22,27,...}
The differences are:
5,5,5,5.
This is an arithmetic sequence following the formula;
a_n = a_1 + (n - 1)d
d is 5
Thus;
a_n = a_1 + (n - 1)5
Now, a_1 = 7. Thus;
a_n = 7 + 5n - 5
a_n = 5n + 2
B) The sequence is given as;
{ 3,7,15,31,63,...}
Now, let's write out the differences of this sequence:
Differences are:
4, 8, 16, 32
This shows that it is a geometric sequence with a common ratio of 2.
In the given sequence, a_1 = 3 and a_2 = 7 and a_3 = 15
Thus, a_2 = 2a_1 + 1
Also, a_(2 + 1) = 2a_2 + 1
Combining both equations, we can deduce that: a_(n + 1) = 2a_n + 1
Thus; a_n can be expressed as:
a_n = (2^(n + 1)) - 1
division problem
In a division problem, the number being divided into pieces is the dividend. The number by which the dividend is divided is called the divisor. And the answer to the division problem is the quotient.
