Question

If A times the 7th term of an AP is equal to 12 times the 12th term then find the 19th term.

Answer 1

$A{T}_r=12\cdot T_{12}$ $T_{19}=a+17d$ ……….$\left(1\right)$

$A(a+6d)=12(a+11d)$

$A(a+6d)=12a+32d$

$Aa+6Ad=12a+132d$

$(12a-Aa)+132d-6Ad=0$

$a(12-A)+d(132-6A)=0$ ……..$\left(2\right)$

On comparing $\left(1\right)$ and $\left(2\right)$:-

$132-6A=17$

$6A=132-17$

$6A=115$

$A=\frac{115}{6}$

$A=\frac{35}{2}$

$12-A=1$

$A=11$

Incomplete question.