What is the t8,t9,t10 of -1,2,5,8
Help me I can't solve it
To find the differences between consecutive terms in the given sequence, we subtract each term from its following term.
For the sequence -1, 2, 5, 8:
The difference between 2 and -1 is 2 - (-1) = 3.
The difference between 5 and 2 is 5 - 2 = 3.
The difference between 8 and 5 is 8 - 5 = 3.
We can see that the differences between consecutive terms are all 3.
To find the 8th, 9th, and 10th terms of the sequence, we can use the pattern of adding 3 to each term:
For the 8th term: 8th term = 8th term in the sequence + 3 * (8 - 1)
8th term = 8 + 3 * 7
8th term = 8 + 21
8th term = 29
For the 9th term: 9th term = 8th term in the sequence + 3 * (9 - 1)
9th term = 29 + 3 * 8
9th term = 29 + 24
9th term = 53
For the 10th term: 10th term = 9th term in the sequence + 3 * (10 - 1)
10th term = 53 + 3 * 9
10th term = 53 + 27
10th term = 80
So, the 8th term is 29, the 9th term is 53, and the 10th term is 80.
To find the terms in the sequence -1, 2, 5, 8, we need to identify the pattern. From -1 to 2, there is an increase of 3. From 2 to 5, there is also an increase of 3. Similarly, from 5 to 8, there is again an increase of 3. Therefore, we can see that the common difference between the terms is 3.
Now, to find the value of the t8 term, we use the formula for the nth term of an arithmetic sequence:
tn = a + (n - 1)d
Where:
tn is the nth term,
a is the first term of the sequence,
n is the position of the term we want to find, and
d is the common difference between the terms.
For t8:
a = -1 (first term)
d = 3 (common difference)
n = 8
Substituting these values into the formula, we have:
t8 = -1 + (8 - 1) * 3
t8 = -1 + 7 * 3
t8 = -1 + 21
t8 = 20
So, the value of the t8 term in the sequence is 20.
Similarly, we can find the values of t9 and t10 using the same formula and substituting the appropriate values:
For t9:
n = 9
t9 = -1 + (9 - 1) * 3
For t10:
n = 10
t10 = -1 + (10 - 1) * 3
By following these steps, you can find the values of t9 and t10 for the given sequence.
a = -1
d = 3
a_n = -1 + (n-1)*3 = 3n-4