Question

In an A.P., the first term is 12 and the common difference is 6. If the last term of the A.P. is 252, then find its middle term.

Answer 1

Given, First term, a = 12

Common difference, d = 6

Last term, a_n = 252

Since, an = a + (n – 1)d

⇒ 252 = 12 + (n – 1) 6

⇒ `240/6` = n – 1

⇒ n = 41

 Middle term = `(n + 1)/2`

= `(41 + 1)/2`

= 21^st term

Now, a₂₁ = a + (21 – 1)d

= 12 + 20 × 6

= 12 + 120

= 132

Hence, middle term is 132.