Final answer:
To find the 15th term of the arithmetic sequence x+7, 4x+10, 7x+13..., use the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. Substitute the given values into the formula to calculate the 15th term.
Step-by-step explanation:
The given arithmetic sequence is x+7, 4x+10, 7x+13, ...
To find the 15th term, we need to determine the general formula for the sequence. The common difference is the difference between consecutive terms, which in this case is 4x+10 - x+7 = 3x+3.
So, the nth term is given by:
an = a1 + (n - 1) d
a15 = (x + 7) + (15 - 1) (3x + 3)
a15 = 4x + 10 + 14(3x + 3)
a15 = 4x + 10 + 42x + 42
a15 = 46x + 52