The 21st term of the AP- -21- -21-2- 0- 21-2- 21- is

AP: nbsp; –21, 21/2, 0, 21/2, 21,..... Here a = 21 and d = 21/2 ( 21) = 21/2 + 21 = 21/2 Now, a_n = a + (n – 1)d a_21 = a + (21 – 1)d = –21 + 20 ×21/2 = ...

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Standard X

Mathematics

nth Term of an AP

The 21st term...

Question

The $21^{s t}$ term of the AP: $- 21, \frac{- 21}{2}, 0, \frac{21}{2}, 21, . . . . .$ is

210

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189

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168

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231

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Solution

The correct option is B 189
AP: $- 21, \frac{- 21}{2}, 0, \frac{21}{2}, 21, . . . . .$
Here $a = - 21$
and $d = \frac{- 21}{2} - (- 21) = \frac{- 21}{2} + 21 = \frac{21}{2}$
Now, $a_{n} = a + (n - 1) d$
$a_{21} = a + (21 - 1) d = - 21 + 20 \times \frac{21}{2}$
$= - 21 + 10 \times 21$
$= - 21 + 210$
$= 189$
Hence, the correct answer is option (2).

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The 21st term of the AP: –21,−212,0,212,21,..... is

The correct option is B 189AP: –21,−212,0,212,21,..... Here a=−21 and d=−212−(−21)=−212+21=212 Now, an=a+(n–1)d a21=a+(21–1)d=–21+20×212 =–21+10×21 =–21+210 =189 Hence, the correct answer is option (2).

The $21^{s t}$ term of the AP: $- 21, \frac{- 21}{2}, 0, \frac{21}{2}, 21, . . . . .$ is