We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

Forgot how to do this......

Find the fourth arithmetic means between -21 and -36

quilly Apr 5, 2018

#1**0 **

**Find the fourth arithmetic means between -21 and -36**

\(\text{We use $a_n = a_1 + (n-1)d$ to find the common difference $d$.} \)

**Solution**

\(\text{The first term is $a_1 = - 21$ and the fourth term is $a_4 = - 36 $.}\\ \text{We must find the common difference so that the terms }\)

\(\begin{array}{cccc} -21, & -21+d, & -21+2d, & -36 \\ \uparrow & \uparrow & \uparrow & \uparrow \\ a_1 & a_2 & a_3 & a_4 \end{array}\)

\(\text{form an arithmetic sequence.} \)

\(\text{To find the common difference $d$, we substitue $-21$ for $a_1$; 4 for $n$, and $-36$ for $a_n \\$in the formula for the 4th term:}\)

\(\begin{array}{rcll} a_4 &=& a_1 + (n-1)d \qquad & \text{This gives the 4th term of any arithmetic sequence.} \\ -36 &=& -21 + (4-1)d \qquad & \text{Substitute.} \\ -36 &=& -21 + 3d \qquad & \text{Subtract within the parentheses.}\\ -15 &=& 3d \qquad & \text{Subtract -21 from both sides.} \\ -5 &=& d \qquad & \text{To isolate d, divide both sides by 3.} \\ \end{array}\)

\(\text{To find the two arithmetic means between $-21$ and $-36$, $\\$we add the common difference $-5$, as shown:}\)

\(\begin{array}{rcll} -21+d &=& -21 +(-5) \\ &=& -26 \qquad & \text{This is $a_2$.} \\ \end{array}\)

\(\begin{array}{rcll} -21+2d &=& -21 +2(-5) \\ &=& -21 -10 \\ &=& -31 \qquad & \text{This is $a_3$.} \\ \end{array}\)

\(\text{Two arithmetic means between $-21$ and $-36$ are $-26$ and $-31$.} \)

heureka Apr 5, 2018