What is the 32nd term of the arithmetic sequence where a1 = -33 and a9 = -121?
What is the sum of a 22-term arithmetic sequence where the first term is 57 and the last term is -27?

Question

What is the 32nd term of the arithmetic sequence where a1 = -33 and a9 = -121?
What is the sum of a 22-term arithmetic sequence where the first term is 57 and the last term is -27?

campbell_st · Answer

1st task is to find the common difference

use theformula for  a term in an arthmetic sequence$$T _{n}=a+(n-1)d$$

use term 9

$$-121 = -33 +(9 -1)d$$

-121 = -33 + 8d

-88 = 8d

d = 8

the common difference for the sequence is 8


use the above formula to find the 32 term$$T _{32} = -33 + (32-1)\times(-8)$$

you can evaluate it

sum of an arthmetic series is $$s _{n}=\frac{n}{2}(a + l)$$

n = number of terms a = 1st term l = last term

anonymous · Answer

I got -281 but that is not one of my options.

campbell_st · Answer

for the sum of the term

campbell_st · Answer

oops calculation error the common difference is d = -11 and not 8

campbell_st · Answer

-88 = 8d  then d = -11