If the sum of first n term is 1600,and the
common different is 2 while the 1st term is 1.find n?
40
To find the value of n, we need to 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, and n is the number of terms.
Given that the sum of the first n terms is 1600, a = 1, and d = 2, we can substitute these values into the formula:
1600 = (n/2)(2 * 1 + (n-1) * 2)
Simplifying this equation:
1600 = (n/2)(2 + 2n - 2)
1600 = (n/2)(2n)
Divide both sides of the equation by 2:
800 = n^2
Take the square root of both sides:
√800 = √(n^2)
Now, we have two possible values for n: +√800 and -√800. Since we are looking for a positive value for n, we discard the negative root.
√800 ≈ 28.28
Therefore, n ≈ 28.28
However, since n represents the number of terms in a series, it must be a whole number. We round the approximation of n down to the nearest whole number:
n = 28
So, the number of terms in the series is 28.