Question

Consider the sequence 130, 143, 156, 169, ...    Write an explicit formula to represent the arithmetic sequence and use it to find the 13th term. 

A. A(n) = 130 + (n-1)13; 286

B. A(n) = 130 + 13n; 299

C. A(n) = 130 + 13n; 286

D. A(n) = 130 + (n-1)13; 299

please help

Answer 1

A(n)=130+13(n-1) ; 86

Explanation:

Here is the sequence

130,143,156,169.......

the first term denoted by a is 130 and the common difference denoted by d is second term minus first term

143 - 130 = 13

Hence a=130 and d = 13

Now we have to evaluate to 13th term.

The formula for nth term of any Arithmetic Sequence is

A(n) = a+(n-1)d

Hence substituting the values of a ,and d get

A(n)=130+13(n-1)

To find the 13th term , put n = 13

A(13)=130+13*(13-1)

= 130+13*12

= 130+156

A(13) = 286