If 3,p,q,24 are consecutive terms of a linear sequence, find the values of p and q.
since there is a common difference,
p-3 = q-p
q-p = 24-q
Solve for p and q.
Or, since the 4th term is a+3d, 3d = 24-3 = 21.
Now you have d, so just use that to generate each term.
To find the values of p and q in the given linear sequence, we need to first determine the common difference between the terms. In a linear sequence, the common difference (d) is the difference between any two consecutive terms.
In this case, we are given that 3, p, q, and 24 are consecutive terms. Therefore, we can set up two equations using the given information:
p = 3 + d
q = p + d
Now, we substitute the value of p from the first equation into the second equation:
q = (3 + d) + d
q = 3 + 2d
Since the last term of the sequence is 24, we can set up another equation:
24 = q + d
Now we can substitute the value of q from the previous equation into this equation:
24 = (3 + 2d) + d
24 = 3 + 3d
21 = 3d
d = 7
Now that we have the value of d, we can substitute it back into the equations to find the values of p and q:
p = 3 + d
p = 3 + 7
p = 10
q = p + d
q = 10 + 7
q = 17
Therefore, the values of p and q are 10 and 17, respectively.