To find the 1st difference between the given terms in the sequence, we can follow these steps:
1. First, plug in the value of [tex]\( a = 1 \)[/tex] into both the second and third term expressions:
- The second term is given by [tex]\( 3a + 5 \)[/tex]:
[tex]\[
a_2 = 3(1) + 5 = 3 + 5 = 8
\][/tex]
- The third term is given by [tex]\( 8a - 3 \)[/tex]:
[tex]\[
a_3 = 8(1) - 3 = 8 - 3 = 5
\][/tex]
2. Next, calculate the 1st difference, which is the difference between the third term and the second term:
[tex]\[
\text{1st Difference} = a_3 - a_2 = 5 - 8
\][/tex]
3. Simplify the result:
[tex]\[
\text{1st Difference} = -3
\][/tex]
Therefore, the 1st difference is [tex]\( -3 \)[/tex].
