If 8, A, B, C, D, 38, 44, 50, ... provides all the A.P. Find the values of A, B, C and D.

Question: If 8, A, B, C, D, 38, 44, 50, ... provides all the A.P. Find the values of A, B, C and D.

Solution

Given the A.P.:

Step 1: Identifying the common difference ($d$)

We know that in an A.P., the difference between consecutive terms is constant.

From the last three terms:

So, the common difference $d = 6$.

Step 2: Finding the missing terms

Now, we backtrack to find the missing terms.

• $D = 38 - 6 = 32$
• $C = 32 - 6 = 26$
• $B = 26 - 6 = 20$
• $A = 20 - 6 = 14$

Thus, the missing values are: