A linear sequence starts a+3b a+7b a+11b the 2nd term has value 19 the 5th term has value 67 work out the values of a and b

Step-by-step explanation:

Given

Sequence: a+3b, a+7b, a+11b

2nd term = 19

5th term = 67

Required

Find a and b

First, the 5th term needs to be calculated;

Using formula for Arithmetic Progression (AP), the formula goes thus

Where n = 5

T_1 = a + 3b ------------ FIrst term

--- Difference between two successive terms

So, becomes

Now that we have values for 2nd and 5th term;

From the second, T2 = 19 and T5 = 67

This gives

--- Equation 1

---- Equation 2

Make a the subject of formula in (1)

Substitute these values in equation 1

becomes

Collect like terms

Divide both sides by 12

Recall that b = 4

Substitute a = 19 - 7b and nothing will hire

Hence, the values of a and b are -9 and 4 respectively.

x=half

step-by-step explanation: