Question

Assuming the pattern continues, what is s12 for the series -5-14-23-32-...?

Answer 1

S₁₂ = - 654

Explanation:

there is a common difference between consecutive terms , that is

- 14 - (- 5) = - 23 - (- 14) = - 32 - (- 23) = - 9

this indicates the series is arithmetic with sum to n terms

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = - 5 and d = - 9 , then

S₁₂ =
`(12)/(2)` [ (2 × - 5) + (11 × - 9) ]

= 6(- 10 - 99 )

= 6 × - 109

= - 654