Question

Find the four arithmetic means between 12 and -13.
A. 6, -1, -3, -8
B. 6, 2, -3, -8
C. 7, -1, -3, -8
D. 7, 2, -3, -8

Answer 1

\[a _{1} ,a _{2} ,a _{3} ,a _{4}~be ~four~arithmetic~means~between~12,-13\]

Answer 2

then \[12,a _{1} ,a _{2} ,a _{3} ,a _{4} ,-13 ~are~in~A.P.\]
a=12
l=-13
no. of terms n=6
let d be c.d.
l=a+(n-1)d
-13=12+(6-1)d
-25=5d
\[d=\frac{ -25 }{ 5 }=-5\]
\[a _{1}=12+d=12-5=7,a _{2}=7+d=7-5=2,\]
\[a _{3}=2+d=2-5=-3\]
\[a _{4}=-3+d=-3-5=-8\]