Mathematics
The 8th term from the end of the A.P. 7, 10, 13, …, 184 is:
157
160
163
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)
⇒ = (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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