Question

The rule for finding the next term in a different sequence is to multiply the previous term by 2 and then add on a, where a is an integer.

The first term is 8 and the fourth term is 127
8, ....., ....., 127
Work out the value of a.

Answer 1

Step 1: Find the second and third terms of the sequence:

Multiply the first term (8) by 2 and add on the unknown value of a: 8 × 2 + a = 16 + a

Step 2: To find the fourth term (127), multiply the third term by 2 and add on a: (16 + a) × 2 + a = 32 + 2a + a = 127

Step 3: Solve for a by subtracting 32 and 2a from both sides: 127 - 32 - 2a = a

Step 4: Simplify the equation to find the value of a: 95 = a

Therefore, the value of a is 95.