Question

The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15th term
NCERT Class X
Mathematics - Exemplar Problems
Chapter _ARITHMETIC PROGRESSIONS

Answer 1

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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