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Answer:
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.