# 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

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.

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1. thongdat2
There are 18 terms are in her series

### What is Arithmetic progression series?

Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value.
Given that: t(n) = −9 + 21n=l
a= 12, Sum = 3429
As, Sum of series =3429
n/2 (a+l) =3429
n/2 (12 +21n-9)= 3429
n/2 (3+21n)=3429
21n² + 3n= 6858
21n² + 3n- 6858=0
7n² + n- 2286=0
For solving for n, get
n= 18 or n= -127/7
Thus, there 18 terms in the series.