What is the sum of the first 16 terms of the AS 11,15,15,33...? Find the last term of the general term and S16.
A. An
B. General term
C. S16
11,15,15,33...
do not form an arithmetic sequence.
Check your typing.
11,15,17,33.. *
Not much better. Still no common difference or ratio.
The differences are 4,2,16
Not much pattern there that I can see. How does 37 look?
To find the sum of the first 16 terms of the arithmetic sequence 11, 15, 15, 33..., we first need to find the common difference in the sequence.
The common difference (d) is the difference between any two consecutive terms in the sequence. We can calculate this by subtracting any term from its previous term.
d = term2 - term1 = 15 - 11 = 4.
Now that we know the common difference, we can find the last term (An) of the arithmetic sequence using the formula:
An = a1 + (n - 1) * d,
where a1 is the first term, n is the number of terms, and d is the common difference.
In this case, we have a1 = 11, n = 16, and d = 4.
An = 11 + (16 - 1) * 4 = 11 + 15 * 4 = 11 + 60 = 71.
Therefore, the last term of the general term is 71, which corresponds to option A.
To calculate the sum of the first 16 terms (S16), we can use the formula for the sum of an arithmetic series:
S16 = (n / 2) * (a1 + An),
where n is the number of terms, a1 is the first term, and An is the last term.
In this case, we have n = 16, a1 = 11, and An = 71.
S16 = (16 / 2) * (11 + 71) = 8 * 82 = 656.
Therefore, the sum of the first 16 terms (S16) is 656, which corresponds to option C.