How do you go from 455=17n+5n2, which is correct,Daaniyaal said:Homework Statement
How many terms are needed in the series 11+16+21+26...+ to exceed 450
d=5
Homework Equations
Sn=n/2(2u1+(n-1)d)
The Attempt at a Solution
(455 because is term exceeding 450 by the d of 5)
455=n/2(22+5n-5)
455=17n+5n2
455/17=5n2
Calculator work,
but the answer I get is not 12. The textbook says the answer is 12 :(
The series 11+16+21+26 + ... is an arithmetic series, where each term is calculated by adding 5 to the previous term. In this series, the first term is 11 and the common difference is 5.
The formula for finding the sum of an arithmetic series is Sn = (n/2)(2a + (n-1)d), where n is the number of terms, a is the first term, and d is the common difference. Plugging in the values for this series, we get Sn = (n/2)(2*11 + (n-1)5).
Finding the sum of this series can help us determine the total value of the terms in the series and how they are related. It can also help us solve real-life problems that involve arithmetic sequences.
To exceed 450, we need to find the value of n in the formula Sn = (n/2)(2*11 + (n-1)5) that will give us a sum greater than 450. By plugging in different values of n, we can determine that we need at least 20 terms to exceed 450.
Yes, the formula Sn = (n/2)(2a + (n-1)d) can be used to find the sum of any arithmetic series, where n is the number of terms, a is the first term, and d is the common difference. This formula can be derived from the formula for the sum of a finite geometric series.