Question

What is the explicit rule for the sequence?

47,42,37,32, …



an=42−5n
an=5n+42
an=5n+52
an=52−5n

Answer 1

an=52-5n is the correct answer

Answer 2

General Idea:

Arithmetic sequence is a sequence which have common difference. The
`n^(th)` term of arithmetic sequence is given by the below formula:

`a_n=a_1+(n-1)\cdot d\\ \\ Where:\\ a_1 \; is \; the \; first\; term\; of\; the\; sequence\\ n is \; the\; number \; of\; terms\; in\; the\; sequence\\ d\; is\; the\; common\; difference\; =\; a_2-a_1`

Applying the concept:

47,42,37,32, …

`a_1=47\\ \\ a_2=42\\ \\ d=a_2-a_1=42-47=-5\\ \\ a_n=47+(n-1) \cdot -5\\ a_n=47-5(n-1)\\ Distributing \; 5\; inside \; the \; parenthesis\\ \\ a_n=47-5n+5\\ Combine\; like\; terms\\ \\ a_n=52-5n`

Conclusion:

The explicit rule for the sequence 47,42,37,32 is
`a_n=52-5n`