We're given the Arithmetic Progression -24, -4, 16, 36 ... .
We know that a term in an AP is generally represented as:
[tex]\bf a_n\ =\ a\ +\ (n\ -\ 1)d[/tex]
where,
- a = the first term in the sequence
- n = the number of the term/number of terms
- d = difference between two terms
We need to find [tex]\sf a_2_3[/tex].
From the given progression, we have:
- a = -24
- n = 23
- d = (-24 - (-4) = -20
Using these in the formula,
[tex]\sf a_2_3\ =\ a\ +\ (n\ -\ 1)d\\\\\\a_2_3\ =\ -24\ +\ (23\ -\ 1)\ \times\ (-20)\\\\\\a_2_3\ =\ -24\ +\ 22\ \times (-20)\\\\\\a_2_3\ =\ -24\ -\ 440\\\\\\\bf a_2_3\ =\ -464[/tex]
Therefore, the 23rd term in the AP is -464.
Hope it helps. :)
