SOLUTION: 1)Find the sum of the arithmetic sequence 2, 4, 6, 8, ..., 70. 2)Find the sum of the geometric sequence 42, 7, 7/6, .... , 42(1/6)^8 3)find the sum of the first n terms of t

Algebra ->  Sequences-and-series -> SOLUTION: 1)Find the sum of the arithmetic sequence 2, 4, 6, 8, ..., 70. 2)Find the sum of the geometric sequence 42, 7, 7/6, .... , 42(1/6)^8 3)find the sum of the first n terms of t      Log On


   

Question 631827: 1)Find the sum of the arithmetic sequence 2, 4, 6, 8, ..., 70.
2)Find the sum of the geometric sequence 42, 7, 7/6, .... , 42(1/6)^8
3)find the sum of the first n terms of the sequence. The sequences are either arithmetic or geometric. -1, 11, -121, ...; n = 9
4)find the sum of the first n terms of the sequence. The sequences are either arithmetic or geometric. 14, 8, 2,...; n=9
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Arithmetic sequence

In General: a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad  and S%5Bn%5D=%28n%2F2%29%282%2Aa%5B1%5D%2B+%28n-1%29d%29

{2, 4, 6, 8, ..., 70) d = 2  and 2+%2B%28n-1%29%2A2+=+70 n = 35

finding the Sum of the first 35 Terms: S%5B35%5D=%2835%2F2%29%282%2A2%2B+34%2A2%29+=+%2835%2F2%29%2A72+=+1260+

14, 8, 2,...; n=9   d = -6

finding the Sum of the first 9 Terms:S%5B9%5D=%289%2F2%29%282%2A14%2B+%288%29%2A-6%29+=+%289%2F2%29%28-20%29+=+-90



Geometric sequence

In General: a%5Bn%5D+=+a%5B1%5D%2Ar%5Ehighlight%28%28n-1%29%29   and S%5Bn%5D=+a%5B1%5D%28%281-r%5En%29%2F%281-r%29%29

Find the sum of the geometric sequence 42, 7, 7/6, .... , highlight%2842%281%2F6%29+%5E8%29 r+=+1%2F6 and last term is the 9th Term

finding the Sum of the first 9 Terms:S%5B9%5D=+42%28%281-%281%2F6%29%5E9%29%2F%285%2F6%29%29 using 42%2F%285%2F6%29=+50.4 as %281%2F6%29%5E9 is so insignificant

-1, 11, -121, ...; n = 9 , r = -11 :

finding the Sum of the first 9 Terms: S%5B9%5D=+-1%28%281-%28-11%29%5E9%29%2F%2812%29%29

will Let You finish this one out