Show Work:
find a20
a1=16 a4=2
find a20
a1=16 a4=2
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3d = a4 - a1 = 2 - 16 = -14
d = -14/3
a20 = a1+19d = 16 + 19(-14/3) = -218/3
d = -14/3
a20 = a1+19d = 16 + 19(-14/3) = -218/3
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To mather,
T(20) = 16 + (10 - 1) * (-14/3) is incorrect.
T(20) = 16 + (10 - 1) * (-14/3) is incorrect.
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There is a formula for this.
T(n) = T₁ + (n - 1) * d but first you use a₁ and a₄ to find d (the common difference) Keep in mind that T₁ = a₁ and T₄ = a₄ and T(20) = a(20)
For a₄ n = 4 so we can set up the formula like this:
T₄ = T₁ + (4 - 1) * d if we plug in the values we know for a₁ and a₄
2 = 16 + 3d. solving for d we get
3d = -14
d = -14/3 so now our equation becomes
T(n) = T₁ + (n - 1) * (-14/3) you can now use this formula to find any term of the sequence. To find a(20) ( also known as T(20) ), we just use the formula with n = 20.
T(20) = 16 + (10 - 1) * (-14/3)
T(20) = 16 + 9*(-14/3) = 16 - 42
T(20) = -26
T(n) = T₁ + (n - 1) * d but first you use a₁ and a₄ to find d (the common difference) Keep in mind that T₁ = a₁ and T₄ = a₄ and T(20) = a(20)
For a₄ n = 4 so we can set up the formula like this:
T₄ = T₁ + (4 - 1) * d if we plug in the values we know for a₁ and a₄
2 = 16 + 3d. solving for d we get
3d = -14
d = -14/3 so now our equation becomes
T(n) = T₁ + (n - 1) * (-14/3) you can now use this formula to find any term of the sequence. To find a(20) ( also known as T(20) ), we just use the formula with n = 20.
T(20) = 16 + (10 - 1) * (-14/3)
T(20) = 16 + 9*(-14/3) = 16 - 42
T(20) = -26