5th term of -13,19,231,1031
To find the 5th term of the sequence -13, 19, 231, 1031, we can observe that each term is obtained by multiplying the previous term by 10 and then subtracting a specific number.
Let's denote the first term as a₁, the second term as a₂, and so on.
a₁ = -13
a₂ = 19
a₃ = 231
a₄ = 1031
To find the 5th term, we need to multiply the 4th term by 10 and subtract a certain number.
a₅ = 10 * a₄ - x
To determine the subtracted value, we can analyze the pattern between adjacent terms.
a₂ - a₁ = 19 - (-13) = 32
a₃ - a₂ = 231 - 19 = 212
a₄ - a₃ = 1031 - 231 = 800
We can see that the difference between adjacent terms is increasing by a factor of 10 each time. Thus, the subtracted value for the 5th term would be (800 * 10) + 212, which is equal to 8212.
Therefore, the 5th term of the sequence is:
a₅ = 10 * a₄ - x
a₅ = 10 * 1031 - 8212
a₅ = 10310 - 8212
a₅ = 2098
To find the 5th term of the given sequence -13, 19, 231, 1031, we can observe that the pattern of the sequence is multiplying each term by a constant and then adding a specific number.
The difference between each term is increasing by a constant value.
Let's first find the common difference by subtracting each consecutive term:
19 - (-13) = 32
231 - 19 = 212
1031 - 231 = 800
Now, let's find the common difference of the differences:
32 - 32 = 0
212 - 32 = 180
800 - 212 = 588
The common difference of the differences is 588.
Next, we can find the common ratio by dividing each term by the previous term:
19 / (-13) = -1.4615
231 / 19 = 12.1579
1031 / 231 = 4.4719
Now, let's find the common ratio of the ratios:
-1.4615 / 12.1579 = -0.1200
12.1579 / 4.4719 = 2.7183
The common ratio of the ratios is approximately 2.7183.
Now, to find the 5th term, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
where:
an is the nth term,
a1 is the first term,
r is the common ratio, and
n is the position of the term we are trying to find.
Plugging in the values:
a1 = -13
r = 2.7183
n = 5
a5 = -13 * (2.7183)^(5-1)
Simplifying the expression:
a5 = -13 * (2.7183)^4
Calculating the value:
a5 = -13 * 54.5980
a5 is approximately -709.774
Therefore, the 5th term of the sequence -13, 19, 231, 1031 is approximately -709.774.
To find the 5th term of the given sequence, you can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
Where:
an = nth term
a1 = first term
d = common difference
In this case, let's find the common difference (d):
d = a2 - a1 = 19 - (-13) = 32
Now, substitute the values into the formula to find the 5th term (a5):
a5 = -13 + (5-1) * 32
= -13 + 4 * 32
= -13 + 128
= 115
Therefore, the 5th term of the given sequence is 115.