Question

if 7 times the 7 term of AP Is equal to 11 times its 11 term show 18 term is 0​

Answer 1

$\bold{Given:-} \begin{cases} \sf{ 7(a_7) = } \\ \sf{11(a_{11})} \end{cases}$

${ \underline{ \large{Solution:-}}}$

$7(a_7) = 11(a_{11}). \\ \\ \implies \: 7(a + 6d) = 11(a + 10d). \\ \\ \implies \: 7a + 42d = 11a + 110d. \\ \\ \implies \: - 4a = 68d. \\ \\ \implies \: a = \frac{ - 68d}{4} .$

$\purple { \underline{\large{ \boxed{ a = \frac{ - 68d}{4} }}}}$

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$a_{18} = a + 17d. \\ \\ \implies \: - \frac{68d}{4} + 17d. \\ \\ \implies \: \frac{ - \cancel{68d} + \cancel{68d}}{ 4} . \\ \\ \implies \: \frac{0}{4} . \\ \\ \implies \: 0$

$\pink {\huge{ \boxed{a_{18} = 0}}}$

Hence Proved.