Progression Practice Test 1

Let ${\mathit{a}}_1,{\mathit{a}}_2,{\mathit{a}}_3$ , be three arithmetic mean between 11 and 12
So, the AP series is $11,{\mathit{a}}_1,{\mathit{a}}_2,{\mathit{a}}_3,12$
a is the first term and d is the common difference of AP. Then a = 11
${\mathit{t}}_5=\mathit{a}+5\mathit{d}$
$\Rightarrow 12=11+5\mathit{d}$
$\Rightarrow \mathit{d}=\frac{1}{5}$
$\therefore {\mathit{a}}_1=11+\mathit{d}=11+\frac{1}{5}=\frac{56}{5}$
${\mathit{a}}_2=11+2\mathit{d}=11+\frac{2}{5}=\frac{57}{5}$
${\mathit{a}}_3=11+3\mathit{d}=11+\frac{3}{5}=\frac{58}{5}$
Hence, the required arithmetic means are $\frac{56}{5},\frac{57}{5},\frac{58}{5}$