The fourth and tenth terms of an AP are defined by: T4=7x+8 and T10=19x+14 (a) Determine expressions for the first term and the common difference (b) If the sum of the fifteen terms of this progression is 630, what is the value of the thirtieth term?
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answer B is given A is below sorry for not providing in order
A - T10 = a + 9d = 19x +14. - ( 1 equation )
T 4 = a + 3d = 7x + 8. - (2 equation)
(1 equation) - (2 equation) = 6d = 12x + 6
d = 2x + 1
By substituting the value of d in (2),
a + 3*(2x + 1) = 7x + 8
a = 7x + 8 - 6x -3 = x + 5
The expression for first term, a = (x + 5) &
d = (2x+1).
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