Question

Choose two of the following choices that can represent the nth term of the sequence: 4, 7, 10, 13, ...

a_n=4n+3, n≥1

a_n=3n+4, n≥1

a_n=4+(n-1)*3, n≥1

a_n=3n+1, n≥1

a_n=3+(n-1)*4, n≥1

Answer 1

Answer: $t_{n}$ = 3n + 1 ,       n≥ 1

Step-by-step explanation:

The common difference of the sequence = 3 , so it is an arithmetic sequence.

The formula for the nth term of an arithmetic sequence is given as:

$t_{n}$ = a + (n-1)d

substituting the values of a and d , we have

$t_{n}$ = 4 + (n-1) X 3

$t_{n}$ = 4 + 3n - 3

$t_{n}$ = 1 + 3n

$t_{n}$ = 3n + 1 ,       n≥ 1