Which term of the A.P. 3, 8, 13,… is 248?

1.	Which term of the A.P. 3, 8, 13,… is 248?
Answer» Given, A.P is 3, 8, 13,… Here, a₁ = a = 3, a₂ = 8 Common difference, d = a₂ – a₁ = 8 – 3 = 5 We know, a_n = a + (n – 1)d Where a is first term or a1 and d is common difference ∴ a_n = 3 + (n – 1)⁵ ⇒ a_n = 3 + 5n – 5 ⇒ a_n = 5n – 2 Now, To find which term of A.P is 248 Put a_n = 248 ∴ 5n – 2 = 248 ⇒ 5n = 248 + 2 ⇒ 5n = 250 ⇒ n = \(\frac{250}{5}\) ⇒ n = 50 Hence, 50^th term of given A.P is 248.

Answer»

Given,

A.P is 3, 8, 13,…

Here,

a₁ = a = 3,

a₂ = 8

Common difference,

d = a₂ – a₁

= 8 – 3

= 5

We know,

a_n = a + (n – 1)d

Where a is first term or a1 and d is common difference

∴ a_n = 3 + (n – 1)⁵

⇒ a_n = 3 + 5n – 5

⇒ a_n = 5n – 2

Now,

To find which term of A.P is 248

Put a_n = 248

∴ 5n – 2 = 248

⇒ 5n = 248 + 2

⇒ 5n = 250

⇒ n = \(\frac{250}{5}\)

⇒ n = 50

Hence,

50^th term of given A.P is 248.

Discussion