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 serie

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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 serie

s 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.

Mathematics

1 answer:

mafiozo [28] · Answer 1 · 2023-01-24T01:37:51+03:00

There are 18 terms are in her series

<h3>What is Arithmetic progression series?</h3>

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.