The formula to find the general term of an arithmetic sequence is,
[tex] a_{n} =a_{1} +(n-1)d [/tex]
Where [tex] a_{n} [/tex]= nth term and
[tex] a_{1} [/tex] = First term.
Given, a9 = −121. Therefore, we can set up an equation as following:
[tex] -33+(9-1)d = -121 [/tex] Since, a1 = -33
- 33 + 8d = -121
-33 + 8d + 33 = -121 + 33 Add 33 to each sides of the equation.
8d = -88.
[tex] \frac{8d}{8} =\frac{-88}{8} [/tex] Divide each sides by 8.
So, d = - 11.
Now to find the 32nd terms, plug in n = 32, a1 = -33 and d = -11 in the above formula. So,
[tex] a_{32} = -33 +(32 -1) (-11) [/tex]
= -33 + 31 ( -11)
= - 33 - 341
= -374
So, 32nd term = - 374.
Hope this helps you!
