find the 1st diffrence given the second and thord term is 3a+5 thord term is 8a -3 the 1st diffrence is

Answer 1

To find the first difference between the terms, we need to understand what the first difference means in the context of sequences. The first difference is calculated by taking the difference between consecutive terms in a sequence.

Given:

• Second term \( T_2 = 3a + 5 \)
• Third term \( T_3 = 8a - 3 \)

To find the first difference \( \Delta_1 \) between the second term and the third term, we calculate:

\[ \Delta_1 = T_3 - T_2 \]

Substituting the given expressions for \( T_2 \) and \( T_3 \):

\[ \Delta_1 = (8a - 3) - (3a + 5) \]

Now we simplify:

\[ \Delta_1 = 8a - 3 - 3a - 5 \] \[ \Delta_1 = (8a - 3a) + (-3 - 5) \] \[ \Delta_1 = 5a - 8 \]

Thus, the first difference is:

\[ \Delta_1 = 5a - 8 \]