Question

If f(1) = 7 and f(n) = -25 (n - 1) - 1 then find the value of f(5).

Answer 1

The given sequence is 460, 451, 442,...

Let's subtract to find the difference in the sequence.

$451-460=-9$

The difference is -9 (d = -9).

Let's use the formula for arithmetic sequences to find the 37th term (n = 37).

$a_n=a_1+(n-1)d$

Where a1 = 460, n = 37, and d = -9.

$\begin{gathered} a_{37}=460+(37-1)\cdot(-9) \\ a_{37}=460+(36)(-9) \\ a_{37}=460-324 \\ a_{37}=136 \end{gathered}$

Therefore, the 37th term is 136.