Find S15 for the series -1 + -3 + -5 + -7 +...

Question

campbell_st · Answer

well you need to common difference... or what is happening to the previous term to get the next. 

the formula is 

$$S_{15} = \frac{n}{2}[2a + (n - 1)d]$$

you know the number of terms   n = 15, the 1st term a = -1 and before you can find the sum, you need the common difference d = 

substitute the values and evaluate

anonymous · Answer

i dont understamd

campbell_st · Answer

Ok... so whats happening in the pattern... -1, -3, -5, ...

anonymous · Answer

decreasing by 2

campbell_st · Answer

yep... or -2 

so  the formula is

$$S_{15} = \frac{n}{2}[2a + (n - 1)d]$$

and from you information you have a = -1, n = 15 and d = -2

so substituting you get 

$$S_{15} = \frac{15}{2}\times[2 \times -1 + (15 -1)\times -2]$$

just use order of operation to get your answer

anonymous · Answer

420?

anonymous · Answer

ANd how would you find common ratio?

campbell_st · Answer

ummm I think your answer is a little large

$$S_{15} = \frac{15}{2}[ -2  -28] $$

which is 

$$S_{15} = \frac{15}{2} [ -30] = 15 \times -15 = -225$$

campbell_st · Answer

the common ratio occurs in geometric series when terms are multiplied by the same number

here is an example

2, 4, 8, 16, 32, .... 

a term is multiplied by 2 to get the next term 

an easy way to check is   term2/term1 does it equal term3/term2

                                         4/2 = 8/2             both are 2 so the common ratio is 2

hope this helps