## mathmath333 one year ago Question

1. anonymous

?

2. mathmath333

In Arithmetic Progression \large \color{black}{\begin{align} S_{15}=150, \ S_{25}=200 ,\ S_{n}=0,\ n=?\hspace{.33em}\\~\\ \end{align}}

3. anonymous

God its been a while since I have done this I would be no help to you sorry

4. hartnn

so you know the sum of Arithmetic series formula ?

5. mathmath333

$$n/2\left(2a+(n-1)d\right)$$

6. hartnn

so with the given data, can we form 2 equations in 2 unknowns and solve for 'a' and 'd' ?

7. mathmath333

yes

8. hartnn

150 = 15 (a+ 7d) 200 = 25 (a+ 12d) right ?

9. mathmath333

yes

10. hartnn

so what values did u get for a and d ?

11. mathmath333

$$a=64/5,d=-2/5$$

12. hartnn

for Sn = 0 2a+(n-1)d = 0 [because n can't be 0]

13. mathmath333

oh yes

14. hartnn

so n is?

15. mathmath333

|dw:1434473688893:dw|

16. mathmath333

:)

17. hartnn

$$\Huge \checkmark$$