Question

Decide whether the given sequence 24,17,10,3...is an A.P.? If yes

find its common term (tn) .​

Answer 1

$\textbf{Given:}$

$\textsf{Sequence is}$

$\mathsf{24,17,10,3,\;.\;.\;.\;.\;.}$

$\textbf{To find:}$

$\textsf{Whether the given sequence is an A.P or not}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{24,17,10,3,\;.\;.\;.\;.\;.}$

$\mathsf{t_2-t_1=17-24=-7}$

$\mathsf{t_3-t_2=10-17=-7}$

$\mathsf{t_4-t_3=3-10=-7}$

$\implies\textsf{Differences are equal}$

$\therefore\textsf{The given sequnce is an A.P}$

$\textsf{The n th term of the sequence is}$

$\mathsf{t_n=a+(n-1)d}$

$\implies\mathsf{t_n=24+(n-1)(-7)}$

$\imlies\mathsf{t_n=24-7n+7}$

$\imlies\boxed{\mathsf{t_n=31-7n}}$

$\textbf{Find more:}$

For an A.P. the first term (a) = 8 common difference (d) = -5 find t2, and t3​

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