the nth term of a series is 9n-7. what is the result of subtracting the kth term from the (k+1)th term?
(with solution pls, thnx)
looks like we can just substitute and evaluate
term(n ) = 9n-7
term(k+1) = 9(k+1) - 7 = 9k + 2
term(k) = 9k - 7
so term(k+1) - term(k)
= 9k+2 - (9k-7) = 9
To find the result of subtracting the kth term from the (k+1)th term, we need to substitute the given expression for the nth term into the equation.
The nth term of the series is given by the formula:
T_n = 9n - 7
To find the kth term, we substitute k for n:
T_k = 9k - 7
Similarly, to find the (k+1)th term, we substitute (k+1) for n:
T_(k+1) = 9(k+1) - 7
Now, let's subtract the kth term from the (k+1)th term:
T_(k+1) - T_k = (9(k+1) - 7) - (9k - 7)
= 9k + 9 - 7 - 9k + 7
= 9k - 9k + 9 + 7 - 7
= 9
Therefore, the result of subtracting the kth term from the (k+1)th term is always 9.