Question

1) -24, -4, 16, 36, ... Find a23

Answer 1

We're given the Arithmetic Progression -24, -4, 16, 36 ... .

We know that a term in an AP is generally represented as:

$\bf a_n\ =\ a\ +\ (n\ -\ 1)d$

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 $\sf a_2_3$.

From the given progression, we have:

• a = -24
• n = 23
• d = (-24 - (-4) = -20

Using these in the formula,

$\sf a_2_3\ =\ a\ +\ (n\ -\ 1)d\\\\\\a_2_3\ =\ -24\ +\ (23\ -\ 1)\ \times\ (-20)\\\\\\a_2_3\ =\ -24\ +\ 22\ \times (-20)\\\\\\a_2_3\ =\ -24\ -\ 440\\\\\\\bf a_2_3\ =\ -464$

Therefore, the 23rd term in the AP is -464.

Hope it helps. :)