# Find Number of Terms

#### xyz_1965

This question comes from chapter 9 in terms of arithmetic sequences.

#### romsek

MHF Helper
$a_k = 8+3k,~k=1,2,\dots$

$\sum \limits_{k=1}^n~a_k = \sum \limits_{k=1}^n~(8+3k) = \\ 8n + 3 \dfrac{n(n+1)}{2} = \\ 8n + \dfrac 3 2 n^2 + \dfrac 3 2 n = \\ \dfrac 3 2 n^2 +\dfrac{19}{2}n = 1092$

$3n^2 + 19n - 2184 = 0$

$n = \dfrac{-19 \pm \sqrt{(19)^2 + 4(3)(2184)}}{6} = \left(-\dfrac{91}{3},~24\right)$

Obviously we ignore the negative solution to obtain

$n = 24$

#### Debsta

MHF Helper
Or simply use the formula for the sum of n terms of an arithmetic sequence.

#### romsek

MHF Helper
Or simply use the formula for the sum of n terms of an arithmetic sequence.
I hate memorizing formulas.

Monoxdifly