Final answer:
To find the number the two sequences have in common, we set their general terms equal to each other and solve for n. The number they have in common is 404.
Step-by-step explanation:
To find the only number that the two sequences have in common, we need to find the general terms of both sequences and set them equal to each other.
The first sequence starts at 30 and increases by 17 each time. So, the general term for the first sequence is an = 30 + 17(n-1).
The second sequence starts at 950 and decreases by 23 each time. So, the general term for the second sequence is bn = 950 - 23(n-1).
Setting these two general terms equal to each other, we get: 30 + 17(n-1) = 950 - 23(n-1).
Simplifying this equation, we find: 40n = 940.
Dividing both sides by 40, we get n = 23.
Substituting this value of n back into either general term, we find that the number the two sequences have in common is 30 + 17(23-1) = 30 + 17(22) = 30 + 374 = 404.