What is the sum of the first 10 terms of the sequence defined by an = 2n - 3?
To find the sum of the first 10 terms of the sequence defined by an = 2n - 3, we can use the formula for the sum of an arithmetic sequence.
The formula for the sum of an arithmetic sequence is given by:
Sn = (n/2) * (a1 + an),
where Sn is the sum of the first n terms, a1 is the first term of the sequence, and an is the nth term of the sequence.
In this case:
a1 = 2(1) - 3 = -1,
an = 2(10) - 3 = 17,
n = 10.
Substituting these values into the formula, we get:
S10 = (10/2) * (-1 + 17),
S10 = 5 * 16,
S10 = 80.
Therefore, the sum of the first 10 terms of the sequence is 80.
To find the sum of the first 10 terms of the given sequence, you need to find the value of each term and then add them all together. In this case, the sequence is defined by the formula an = 2n - 3.
Let's calculate the value of each term in the sequence. The formula tells us that the nth term of the sequence is given by 2n - 3. So, we can substitute the values of n from 1 to 10 into the formula and calculate the corresponding terms.
For n = 1:
a1 = 2(1) - 3 = -1
For n = 2:
a2 = 2(2) - 3 = 1
For n = 3:
a3 = 2(3) - 3 = 3
For n = 4:
a4 = 2(4) - 3 = 5
For n = 5:
a5 = 2(5) - 3 = 7
For n = 6:
a6 = 2(6) - 3 = 9
For n = 7:
a7 = 2(7) - 3 = 11
For n = 8:
a8 = 2(8) - 3 = 13
For n = 9:
a9 = 2(9) - 3 = 15
For n = 10:
a10 = 2(10) - 3 = 17
Now, sum up all these terms:
-1 + 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 70
So, the sum of the first 10 terms of the sequence defined by the formula an = 2n - 3 is 70.
a = a1 = 2*1-3 = -1
d = an+1-an = (2(n+1)-3)-(2n-3)) = 2
Now just use your sum formula
S10 = 10/2 (2a+9d)