a geometric series has the following properties; the 1st and 2nd have a sum of -4 and the 4th and 5th term have a sum of 108. Find the 1st term and the common ratio of the series. Explain why the series has no sum to infinity.

Question

campbell_st · Answer

so if you look at the formula for each term you get 

a term in a geometric series is 

$$a_{n} = ar^{n -1}$$
a = 1st term and r  is the common ratio

1st and 2nd sum   equation 1

$$a + ar = -4$$   

4th and 5th sum equation 2

$$ar^3 + ar^4 = 108$$   

with a little factoring of the equation  2 you get

$$r^3(a + ar) = 108$$

now substitute equation 1

$$r^3 (-4) = 108$$

now you can solve for r. 

when you get r, substitute it into the 1st equation to find a

hope it helpss

anonymous · Answer

a, ar, ar^2, ar^3 and ar^4 are the first 5 terms

a + ar = -4
ar^3 + ar^4 = 108

solve a = 2 and r = -3

abmon98 · Answer

Thank you so much for your help sourwing and campbell_st