Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).202,198,194,...Find the 37th term.

Answer 1

The first 3 terms of the sequence are 202, 198, 194

Since 198 - 202 = -4

Since 194 - 198 = -4, then

The sequence is Arithmetic and decreases by 4

The rule of the arithmetic sequence is

`a_n=a+(n-1)d`

a is the first term

d is the common difference

n is the position of the term

Since the first term is 202, then

a = 202

Since the common difference is -4, then

d = -4

Since we need to find the 37th term, then

n = 37

Substitute them in the rule above

`\begin{gathered} a_(37)=202+(37-1)(-4) \\ a_(37)=202+(36)(-4) \\ a_(37)=202-144 \\ a_(37)=58_{} \end{gathered}`

The 37th term is 58