the sequence 29, 31, 33, 35, 37.... 49 has 11 terms. Evaluate the related series..
my teacher said its 429 don't see how she got it
sum = #of terms(first + last)/2
= 11(29+49)/2
= 429
I believe you just add 29+31+33+35+37+39+41+43+45+47+49 which are 11 terms =429
To evaluate this series, we need to find the sum of the terms. The first step is to determine the common difference between the terms. Looking at the sequence, we can observe that each term increases by 2.
To find the sum of the series, we 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 series, n is the number of terms, a is the first term, and d is the common difference.
In this case, we are given that n = 11 and a = 29. We also know that d = 2, as each term increases by 2.
Let's substitute these values into the formula:
S11 = (11/2)(2(29) + (11-1)(2))
S11 = (11/2)(58 + 20)
S11 = (11/2)(78)
S11 = 429
Hence, the sum of the series 29, 31, 33, 35, 37.... 49 with 11 terms is indeed 429.