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Mathematics

The 8th term from the end of the A.P. 7, 10, 13, …, 184 is:

  1. 157

  2. 160

  3. 163

  4. 166

AP

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Answer

Given,

a = 7

d = 10 - 7 = 3

an = 184

We know that,

⇒ an = a + (n - 1)d

⇒ an = 7 + (n - 1)(3)

⇒ 184 = 7 + (n - 1)(3)

⇒ 184 - 7 = (n - 1)(3)

⇒ 177 = (n - 1)(3)

⇒ 1773\dfrac{177}{3} = (n - 1)

⇒ n - 1 = 59

⇒ n = 59 + 1

⇒ n = 60.

The 8th term from the end is the (n - 8 + 1)th term from the beginning.

= 60 - 8 + 1

= 53.

⇒ a53 = 7 + (53 - 1)3

= 7 + (52)(3)

= 7 + 156

= 163.

Hence, option 3 is the correct option.

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