The 7th and 20th term of an AP are 34 and 112 respectively .find AP
ScanSolve AI Answer
Step-by-step solution
5 stepsLet's find the first term and common difference to define the AP.
Write the general formula for the nth term of an AP.
aₙ = a₁ + (n - 1)d
where a₁ is the first term and d is the common difference.Use the given information to form two equations.
For the 7th term (a₇ = 34):
a₁ + (7 - 1)d = 34
a₁ + 6d = 34 (Equation 1)For the 20th term (a₂₀ = 112):
a₁ + (20 - 1)d = 112
a₁ + 19d = 112 (Equation 2)Solve the system of equations to find d.
Subtract Equation 1 from Equation 2:
(a₁ + 19d) - (a₁ + 6d) = 112 - 34
13d = 78
d = 78 / 13
d = 6Substitute the value of d into Equation 1 to find a₁.
a₁ + 6d = 34
a₁ + 6(6) = 34
a₁ + 36 = 34
a₁ = 34 - 36
a₁ = -2State the Arithmetic Progression.
The AP starts with the first term a₁ = -2 and has a common difference d = 6.
The terms are: -2, (-2 + 6), (-2 + 2×6), ...
The AP is: -2, 4, 10, 16, ...The Arithmetic Progression is defined by its first term a₁ = -2 and common difference d = 6.
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