Question 1068846: if 3,p,q,34 are consecutive terms of an A.P,find the values of p and q
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The n-th term of an arithmetic progression can be written as:
a_n = a + (n-1)d, where d is the common difference and a is the 1st term.
We don't know where the numbers 3 and 34 lie in the sequence, but we know
that their difference is 3d, since they are 3 places away from each other.
So we have 3d = 31, or d = 31/3.
Since consecutive terms differ by d, we have p = 3 + 31/3 = 40/3 and
q = 40/3 + d = 40/3 + 31/3 = 71/3.
So the four values in the sequence are 3, 40/3, 71/3, 34
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