Let's solve the problem step-by-step to find the 1st difference given the second and third terms.
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. Calculate the 1st difference:
The 1st difference is found by subtracting the second term from the third term.
[tex]\[ T_1 \, \text{difference} = T_3 - T_2 \][/tex]
3. Substitute the given terms:
[tex]\[ T_1 \, \text{difference} = (8a - 3) - (3a + 5) \][/tex]
4. Distribute the negative sign and combine like terms:
[tex]\[ T_1 \, \text{difference} = 8a - 3 - 3a - 5 \][/tex]
5. Combine like terms:
- Combine the [tex]\( a \)[/tex]-terms: [tex]\( 8a - 3a = 5a \)[/tex]
- Combine the constant terms: [tex]\( -3 - 5 = -8 \)[/tex]
6. Result:
[tex]\[ T_1 \, \text{difference} = 5a - 8 \][/tex]
So, the 1st difference is [tex]\( 5a - 8 \)[/tex].
