What is the sum of the first 10 terms of the sequence defined by an = 3n - 3?
term1= 3(1) - 3 = 0
term2 = 3(2) - 3 = 3
term3( = 3(3) - 3 = 6
....
looks like an arithmetic sequence , with a=0 and d = 3
sum(1) = (10/2)(2(0) + 9(3))
= 5(27) = 135
Oh, calculating sums of sequences, huh? Well, let me put on my math clown glasses for this one!
To find the sum of a sequence, we can use the formula S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term.
In this case, the first term (a) is 3(1) - 3 = 0, and the last term (l) is 3(10) - 3 = 27. Substituting these values, we have S = (10/2)(0 + 27) = 135.
So, the sum of the first 10 terms of the sequence is 135. Why do mathematicians never get invited to parties? Because they just don't know how to function properly without their calculators!
To find the sum of the first 10 terms of the sequence defined by an = 3n - 3, we need to find the sum of all the terms from n = 1 to n = 10.
Step 1: Find the first term of the sequence.
Substitute n = 1 into the formula:
a1 = 3(1) - 3 = 0
Step 2: Find the last term of the sequence.
Substitute n = 10 into the formula:
a10 = 3(10) - 3 = 27
Step 3: Find the sum of the first and last terms.
Sum = a1 + a10 = 0 + 27 = 27
Step 4: Find the number of terms in the sequence.
Since the sequence is defined by an = 3n - 3, we can see that n is increasing by 1 for each term. So, the number of terms is equal to the value of the last term (a10 = 27).
Step 5: Use the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is:
S = (n/2)(a1 + an)
Substituting the values we found:
S = (10/2)(0 + 27) = 5(27) = 135
Therefore, the sum of the first 10 terms of the sequence defined by an = 3n - 3 is 135.
To find the sum of the first 10 terms of the sequence defined by an = 3n - 3, we can use the formula for the sum of an arithmetic sequence.
The formula for the sum of the first n terms of an arithmetic sequence is Sn = (n/2)(a1 + an), where Sn is the sum, n is the number of terms, a1 is the first term, and an is the last term.
In this case, we want to find the sum of the first 10 terms, so n = 10.
To find the first term, we substitute n = 1 into the given equation:
a1 = 3(1) - 3
a1 = 0
To find the last term, we substitute n = 10 into the equation:
an = 3(10) - 3
an = 27
Now we substitute these values into the formula for Sn:
Sn = (10/2)(0 + 27)
Sn = 5(27)
Sn = 135
Therefore, the sum of the first 10 terms of the sequence defined by an = 3n - 3 is 135.