Let a4+a8+a12+a16=224. find the sum of first 19 term in sequence.

Without knowing anything about the sequence, this is impossible to answer. But suppose the sequence is arithmetic, in which case each term differs by some constant :

Then we can write

and from the formula above, we see this means the 10th term in the sequence is . But that's all the specific info we can gather about such an arithmetic sequence. If we set the first term to be some unknown , then the sum of the first 19 terms in the sequence would be

If we knew one more term in the sequence, we could determine the value of and derive the value of (if the first term is not immediately given), and then go on to find an exact numeric value for the sum.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

answer: i wpould go with c

step-by-step explanation: