is 13 ?
F. 10.5
G. 14.5
H. 18
J. 21.25
K. 39.5
The sum of the first 4 terms of the arithmetic sequence where the 6th term is 8 and the 10th term is 13 is 14.5.
In an arithmetic sequence, the difference between consecutive terms is constant. This difference is commonly called the common difference. Given that the 6th term is 8 and the 10th term is 13, we can calculate this common difference.
The common difference is (13 - 8) / (10 - 6) = 5 / 4 = 1.25.
The common difference is backward from the 6th term to the first term or we can say the 6th term minus 5 times the common difference will give us the first term. Therefore, the first term is 8 - 5*1.25 = 8 - 6.25 = 1.75.
The sum of the first 4 terms of an arithmetic sequence is given by the formula S = n/2 *[2a + (n-1)*d], where 'n' is the number of terms (in this case 4), 'a' is the first term, and 'd' is the common difference.
Therefore, substituting our known values into the formula gives us: S = 4/2 *[2*1.75 + (4-1)*1.25] = 2*[3.5 + 3.75] = 2*7.25 = 14.5
Answer:
hello
Step-by-step explanation:
none
B.
exactly one
C.
exactly two
D.
infinitely many