Question

Determine the indicated term in the following arithmetic sequences.

1.) a subscript 5: {2, 5, 8, ...}
2.) a subscript 20: {4, 8, 12, ...}
3.) a subscript 18: {0,20,40,60, ...}

Answer 1

Answer:

$a_5= 14$

$a_{20}= 80$

$a_{18}= 340$

Step-by-step explanation:

Solving (a):

We have:

$a_1=2$ --- first term

$d = 5 -2 = 3$ common difference

The 5h term is:

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

$a_5= 2+ (5 - 1)*3$

$a_5= 14$

Solving (b):

We have:

$a_1 = 4$ --- first term

$d = 8 -4 = 4$ common difference

The 20h term is:

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

$a_{20}= 4+ (20 - 1)*4$

$a_{20}= 80$

Solving (c):

We have:

$a_1 = 0$ --- first term

$d = 20 -0 = 20$ common difference

The 18th term is:

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

$a_{18}= 0+ (18 - 1)*20$

$a_{18}= 340$