In an arithmetic sequence,the 11th term is double of the 5th term it's

1.	In an arithmetic sequence,the 11th term is double of the 5th term it's 8th term is 27,find its 18th term ?
Answer» from the QUESTION $A_{11} =2times A_{5}$ ⇒ $a+(11-1d)=a+(5-1)d times2$ ⇒ $a+10d=2a+8d$ ⇒ $a-2a=8d-10d$ ⇒ $-a=-2d$ ⇒ $a=2d$ let the 8TH TERM $a_{8} =a+(8-1)d=27$ be equation (1) ⇒ $27=a+7d$ ⇒ $27=2d+7d$ in substituting $a=2d$ in equation (1) ⇒ $27=9d$ ⇒ $d=3$ ∴ the 18 term ⇒ $a_{18} =a+(18-1)d$ = $a+17d=2d+17(3)$ ⇒ $a_{18} =2d+51$ ⇒ $a_{18} =51+2d$ ⇒ $a_{18} =56$ and $a=5$ since $d=3$ Answer: