Find the 8th term from end of the A.P. 7, 10, 13, ..., 184.

1.	Find the 8th term from end of the A.P. 7, 10, 13, ..., 184.
Answer» Here, a = 7, d = 10 – 7 = 3 and l = 184 where l = a + (n – 1)d Now, to find the 8^th term from the end, we will find the total number of terms in the AP. So, 184 = 7 + (n – 1)(3) ⇒ 184 = 7 + 3n – 3 ⇒ 184 = 4 + 3n ⇒ 180 = 3n ⇒ n = 60 So, there are 60 terms in the given AP. Last term = 60^th Second last term = 60 – 1 = 59^th Third last term = 60 – 2 = 58^th And so, on So, the 8^th term from the end = 60 – 7 = 53^th term So, a_n = a + (n – 1)d ⇒ a₅₃ = 7 + (53 – 1)(3) ⇒ a₅₃ = 7 + 52 × 3 ⇒ a₅₃ = 7 + 156 ⇒ a₅₃ = 163

Answer»

Here, a = 7, d = 10 – 7 = 3 and l = 184

where l = a + (n – 1)d

Now, to find the 8^th term from the end, we will find the total number of terms in the AP.

So, 184 = 7 + (n – 1)(3)

⇒ 184 = 7 + 3n – 3

⇒ 184 = 4 + 3n

⇒ 180 = 3n

⇒ n = 60

So, there are 60 terms in the given AP.

Last term = 60^th

Second last term = 60 – 1 = 59^th

Third last term = 60 – 2 = 58^th

And so, on

So, the 8^th term from the end = 60 – 7 = 53^th term

So, a_n = a + (n – 1)d

⇒ a₅₃ = 7 + (53 – 1)(3)

⇒ a₅₃ = 7 + 52 × 3

⇒ a₅₃ = 7 + 156

⇒ a₅₃ = 163

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