Question

 If a=10 ,d=3, n= 30, Find Sn , if the 30th term is 97​

Answer 1

Step-by-step explanation:

nth term of an AP is given by

t

n

=a+(n−1)d

In the given sequence, 'a' = 10, 'd' = -3, 'n' = 30.

So, 30th term =

t

30

=10+(30−1)(−3)

⟹t

30

=10−87=−77.

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Answer 2

$\Huge\tt\purple{answer:}$

$\sf{ }$

$\bf{Given:}$

$\sf{~~~~~~a=10}$

$\sf{~~~~~~d=3}$

$\sf{~~~~~~n=30}$

$\sf{~~~~~~a_{30}=97}$

$\sf{~~~~~~also,~~a_{n}=97}$

$\sf{~~~~~~\therefore S_{n}={\dfrac{n}{2}}[a+a_{n}]}$

$\sf{:→ S_{30}={\dfrac{30}{2}}[10+97]}$

$\sf{:→ S_{30}=15[107]}$

$\sf{:→ S_{30}={\purple{\underline{\boxed{\bf 1605}}}}}$

$\sf{~~~~\therefore S_{n}={\bf{1605}}}$

$\sf{ }$

$\bf \large \underline{Note} : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf The \: answer \: will \: be \: the \: same ,\: if \: we \: use \: the \: formula : \\ \\ \sf sn = \frac{n}{2}(2a + (n - 1)d) \\ \\ \sf Here \: we \: can \: use \: the \: other \: formula \: as \: a_{n}(last \: term) \\ \sf is \: given. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$