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Lucy is working with a series whose first term is 12 and that is generated by the equation t(n) = −9 + 21n. The sum of her series is 3429. How many terms are in her series? *hint: the last term can be written as -9 + 21n if we say there are n terms. You will need to solve a quadratic equation to solve for n.

Respuesta :

A series is the sum of the terms in a particular sequence. There are 18 terms in the given series generated.

What is a series?

A series is the sum of the terms in a particular sequence. These phrases are often real or complex numbers, but they can be considerably more generic.

Given the first term is 12, while the series is generated by the equation t(n)=−9 + 21n. Also, the sum of the series is 3429. Therefore, the equation of the sum can be written as,

[tex]-9n+21\dfrac{(n^2+n)}{2} = 3429[/tex]

-18n + 21n² + 21n = 6858

21n² + 21n - 18n - 6858 = 0

21n² + 3n - 6858 = 0

7n² + n - 2286 = 0

n=-18.143, 18

Since the value can not be negative, therefore, n is equal to 18.

Hence, there are 18 terms in the given series generated.

Learn more about sequence:

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