In the expression $3 n - 10$ , substitute values $1, 2, 3, 4,$ and $5$ for n and write the value of the expression in order. State, with reason, whether the sequence obtained is an $A . P$ .

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Solution

In the expression, $3 n - 10$ , values $1, 2, 3, 4$ and $5$ for
$1 \Rightarrow 3 (1) - 10 \Rightarrow - 7$

$2 \Rightarrow 3 (2) - 10 \Rightarrow - 4$

$3 \Rightarrow 3 (3) - 10 \Rightarrow - 1$

$4 \Rightarrow 3 (4) - 10 \Rightarrow 2$

$5 \Rightarrow 3 (5) - 10 \Rightarrow 5$

terms are $- 7, - 4, - 1, 2, 5$

$d = - 4 + 7 = - 1 + 4 = 2 - 1 = 5 - 2 = 3$

the sequence is in $A P$ because there is common difference among the terms.

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