Find Sn for d = 7, n = 20, and An = 136
I will assume An is supposed to mean term(n) ??
term(n) = a + (n-1)d
136 = a + 19(7)
a = 3
so sum(n) or your Sn
= (n/2)(2a + (n-1)d )
= (n/2)(6 + 7(n-1) )
= (n/2)( 7n -1 )
or
= (7n^2 - n)/2 or some other variation of that
To find the sum of an arithmetic series, we can use the formula:
Sn = (n/2)(2a + (n-1)d)
where Sn is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.
In this case, we are given:
d = 7 (common difference)
n = 20 (number of terms)
An = 136 (value of the nth term)
We need to find the sum Sn.
Step 1: Find the value of the first term, a.
To find the first term, a, using the value of An and the formula for the nth term of an arithmetic sequence:
An = a + (n-1)d
Plugging in the given values:
136 = a + (20-1)(7)
136 = a + 19(7)
136 = a + 133
a = 136 - 133
a = 3
Therefore, the first term, a, is 3.
Step 2: Calculate the sum, Sn.
Now that we have the values of a, n, and d, we can use the formula for Sn to find the sum.
Sn = (n/2)(2a + (n-1)d)
Sn = (20/2)(2(3) + (20-1)(7))
Sn = 10(6 + 19(7))
Sn = 60 + 1330
Sn = 1390
Therefore, the sum of the arithmetic series is 1390.
To find the sum of the arithmetic series (Sn), we need to use the formula:
Sn = (n/2)(2a + (n-1)d)
where:
Sn is the sum of the arithmetic series
n is the number of terms
a is the first term
d is the common difference
In this case, we are given:
d = 7 (common difference)
n = 20 (number of terms)
An = 136 (value of the nth term)
We can use the formula for the nth term of an arithmetic series to find the first term (a):
An = a + (n-1)d
136 = a + (20-1)7
136 = a + 19(7)
136 = a + 133
a = 136 - 133
a = 3
Now we have the values:
a = 3 (first term)
d = 7 (common difference)
n = 20 (number of terms)
Plugging these values into the formula for Sn:
Sn = (n/2)(2a + (n-1)d)
= (20/2)(2(3) + (20-1)(7))
= (10)(6 + 19(7))
= (10)(6 + 133)
= (10)(139)
= 1390
Therefore, the sum of the arithmetic series is Sn = 1390.