To find the first difference given the second and third terms, we need to calculate the difference between these terms step by step.
1. Identify the given terms:
- The second term [tex]\( T_2 \)[/tex] is [tex]\( 3a + 5 \)[/tex].
- The third term [tex]\( T_3 \)[/tex] is [tex]\( 8a - 3 \)[/tex].
2. Set up the expression for the first difference:
The first difference is calculated by subtracting the second term from the third term.
[tex]\[
\text{First difference} = T_3 - T_2
\][/tex]
3. Substitute the given terms into the expression:
[tex]\[
\text{First difference} = (8a - 3) - (3a + 5)
\][/tex]
4. Simplify the expression step by step:
[tex]\[
\text{First difference} = (8a - 3) - 3a - 5
\][/tex]
5. Combine like terms:
[tex]\[
\text{First difference} = 8a - 3a - 3 - 5
\][/tex]
[tex]\[
\text{First difference} = 5a - 8
\][/tex]
The first difference is [tex]\( 5a - 8 \)[/tex].
