Question

The eight term of an A P is half its second term and the eleventh term exceeds one third of its fourth term by 1 Find the 15th term.

Answer 1

.............I hope it will hlp

Answer 2

$\bf\huge\textbf{\underline{\underline{According\: to\: the\: Question}}}$  

$\sf{\implies a_{8} = \dfrac{1}{2} a_{2}}$

$\sf{\implies a_{11} = \dfrac{1}{3}\times a_{4} + 1}$

${\boxed{\bigstar{\sf\:{Now}}}}$

$\sf{\implies a + 7d = \dfrac{1}{2}\times (a + d)}$

$\sf{\implies a + 10d = \dfrac{1}{3}\times (a + 3d) + 1}$

$\tt{\implies 2a + 14d = a + d \:and\: also\: 3a + 30d = a + 3d + 3}$

${\boxed{\bigstar{\sf\:{a + 13d = 0\:and\:2a + 27d = 3}}}}$

$\textbf{\underline{\underline{Solving\:We\:Get :-}}}$

2(-13d) + 27d = 3

d = 3

a = -13d

a = -13(3)

a = -39

${\boxed{\bigstar{\sf\:{a_{15} = a + 14d}}}}$

= - 39 + 14(3)

= -39 + 42

= 3