what is the sum of the 1st 10 terms of the arithmetic series that has a 10th term of 50 and a 1st term of 5
325
To find the sum of the 10 terms in an arithmetic series, we can use the formula:
Sn = n/2 * (a1 + an)
Where:
Sn is the sum of the n terms,
n is the number of terms,
a1 is the first term, and
an is the nth term.
Given that the 10th term (an) is 50 and the first term (a1) is 5, we can substitute these values into the formula:
Sn = 10/2 * (5 + 50)
Simplifying further:
Sn = 5 * 55
Sn = 275
Therefore, the sum of the first 10 terms of the arithmetic series is 275.
To find the sum of the first 10 terms of an arithmetic series, you can use the formula for the sum of an arithmetic series:
Sn = n/2 * (2a + (n-1)d)
where Sn is the sum of the first n terms, a is the first term, d is the common difference between terms, and n is the number of terms.
In this case, we are given that the 10th term (a10) is 50 and the first term (a1) is 5.
a10 = a1 + (n-1)d
Substituting the given values, we have:
50 = 5 + (10-1)d
Simplifying, we get:
45 = 9d
Dividing both sides by 9, we find:
d = 5
Now we have the first term (a1 = 5), the common difference (d = 5), and the number of terms (n = 10).
Using the formula for the sum of an arithmetic series, we can calculate the sum:
Sn = n/2 * (2a + (n-1)d)
Sn = 10/2 * (2(5) + (10-1)(5))
Sn = 5 * (10 + 9(5))
Sn = 5 * (10 + 45)
Sn = 5 * 55
Sn = 275
Therefore, the sum of the first 10 terms of the arithmetic series is 275.
a = 5
term(10) = a+9d
5+9d = 50
9d = 45
d = 5
so you have a=5 and d=5
can you take it from there?