Question

If 6 times the $6^{th}$ term of an AP is equal to 21 times the ${21}^{st}$ term of that AP, then ${27}^{th}$ term of the same AP is ___

• A. 1
• B. 0.0
• C. -1
• D. -2

Answer 1

The correct option is B 0.0

Given,
$6a_6=21a_{21}$
$\Rightarrow$ 6[a + (6 - 1)d] = 21[a + (21 - 1)d]
$\Rightarrow$ 6(a + 5d) = 21(a + 20d)
$\Rightarrow$ 6a + 30d = 21a + 420d
$\Rightarrow$ -15a - 390d = 0
$\Rightarrow$ 15a + 390d = 0
$\Rightarrow$ a + 26d = 0
$\Rightarrow$ a + (27 - 1)d = 0
Hence, ${27}^{th}$ term of the same AP is 0.