What is the sum of a 22-term arithmetic sequence where the first term is 57 and the last term is -27?
What is the sum of a 6-term geometric series if the first term is 24 and the last term is 1,417,176?

Question

What is the sum of a 22-term arithmetic sequence where the first term is 57 and the last term is -27?
What is the sum of a 6-term geometric series if the first term is 24 and the last term is 1,417,176?

campbell_st · Answer

claire can you write this formula down

sum of an arithmetic series

given 1st and last term

$$s _{n} = \frac{n}{2}(a + l)$$

n = number of terms , a = 1st term l = last term

substitute your information and evaluate

anonymous · Answer

I was not given that formula, I only have a1-a1r^n/1-r.
Thank you!

campbell_st · Answer

Part 2

a term in  geometric series is found using 

$$T _{n} = ar^{n-1}$$

a = 1st term, r = common ratio and n = number of terms

$$1417176=24r^5$$

solve for r

divide by 24

$$r^5 = 59049$$

take the 5th root

r = 9

now use the sum of a geometric series

$$s _{n} = \frac{a(r^n - 1)}{r -1}$$

in your question, a = 24, r = 9 and n = 6

good luck