If you have a typo, and the sequence starts -10, -8, -6, then we clearly have
a = -10
d = 2
So, as with all AP's, the nth term is a + 2(n-1)
the sum of the first n terms is n/2 (2a + (n-1)*d)
so plug in your numbers.
a = -10
d = 2
So, as with all AP's, the nth term is a + 2(n-1)
the sum of the first n terms is n/2 (2a + (n-1)*d)
so plug in your numbers.
b) To find the sum of the first 21 terms, we can use a little math magic. First, let's find the common difference between the terms. From -10 to -8, we add 2. From -8 to 6, we add 14. So it seems like the difference between terms is increasing by 12 each time.
Using this pattern, we can find the 10th term by starting with -10 and adding (10-1) * 12 = 108. So the 10th term is 98.
Now, let's find the sum of the first 21 terms. We can use the arithmetic series formula: Sn = n/2 * (a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term.
Plugging in the values, we get: S21 = 21/2 * (-10 + 98) = 21/2 * 88 = 924.
So, the sum of the first 21 terms is 924. But remember, math is only serious if you subtract the "fun"!
nth term = first term + (n - 1) * common difference
In the given arithmetic progression, the first term is -10, and the common difference is the difference between any two consecutive terms.
To find the common difference, you can subtract any two terms. Let's take the first two terms:
First term: -10
Second term: -8
Subtracting the first term from the second term:
-8 - (-10) = -8 + 10 = 2
Therefore, the common difference is 2.
Now, let's find the tenth term:
n = 10 (since you need the tenth term)
First term = -10
Common difference = 2
Tenth term = -10 + (10 - 1) * 2
= -10 + 9 * 2
= -10 + 18
= 8
So, the tenth term of the given arithmetic progression is 8.
To find the sum of the first n terms of an arithmetic progression, you can use the formula:
Sum of first n terms = (n/2) * (2 * first term + (n - 1) * common difference)
Let's find the sum of the first 21 terms:
n = 21 (since you need the sum of the first 21 terms)
First term = -10
Common difference = 2
Sum of the first 21 terms = (21/2) * (2 * (-10) + (21 - 1) * 2)
= (21/2) * (-20 + 20 * 2)
= (21/2) * (-20 + 40)
= (21/2) * 20
= 21 * 10
= 210
Therefore, the sum of the first 21 terms of the given arithmetic progression is 210.