Final answer:
The sequence follows a recursive formula of an = an-1 + 19 and an explicit formula of an = 19n - 9. Based on these formulas, the correct statements are B, D, and E.
Step-by-step explanation:
To find the pattern in this sequence, we can observe that each term is obtained by adding 19 to the previous term.
Therefore, the recursive formula for this sequence is an = an-1 + 19.
To find the explicit formula, we can use the fact that the first term is 10 and the common difference is 19. Using the formula an = a1 + (n-1)d, where a1 is the first term, d is the common difference, and n is the term number, we can substitute the values to get an = 10 + (n-1)19 = 19n - 9.
Based on these formulas, we can determine the answers to the statements:
A) The 10th term is given by a10 = 19(10) - 9 = 181, which is not equal to 199. So statement A is incorrect.
B) The 15th term is given by a15 = 19(15) - 9 = 276, which is equal to 276. So statement B is correct.
C) The 20th term is given by a20 = 19(20) - 9 = 371, which is not equal to 389. So statement C is incorrect.
D) The recursive formula is an = an-1 + 19, which is correct. So statement D is correct.
E) The explicit formula is an = 19n - 9, which is correct. So statement E is correct.
Therefore, the correct statements are B, D, and E.