Question

how many terms of the ap 27 24 21 .....should be taken so that their sum is zero

Answer 1

See the attach file for ur ans

Answer 2

Answer:

$Sum\: of \: 19 \: terms = 0 \: in \:given\:\\ A.P$

Step-by-step explanation:

$Let\: a\: and\: d\: are\: first \:term\:\\ and \:common \:difference \:of\\ \:an\: A.P$

$In \: given \: A.P : 27,24,21,...$

$a = 27 , \\d= a_{2}-a_{1}\\d=24-27\\d=-3$

$\boxed {Sum \: of \: n \: terms \: (S_{n})\\= \frac{n}{2}[2a+(n-1)d]}$

$S_{n}=0$\* given*\

$\implies \frac{n}{2}[2\times 27+(n-1)(-3)]=0$

$\implies n(54-3n+3)=0\times 2$

$\implies n(-3n+57)=0$

$\implies -3n+57=0$

$\implies -3n = -57$

$\implies n = \frac{-57}{-3}$

$\implies n = 19$

Therefore,

$Sum\: of \: 19 \: terms = 0 \: in \:given\:\\ A.P$

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