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.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.