Question

in an AP the first term is 12 and the common difference is 6 if the last term of AP is 252 find its middle term please tell the solution please

Answer 1

Given: First term = a = 12

Common difference = d =6 and

last term of A.P. = 252

Let there be n terms in given A.P.

 

⇒ an = 252

⇒ a + (n – 1) d = 252

⇒12+ (n – 1)6 = 252

⇒(n – 1) 6 = 240

⇒n – 1 = 40

⇒ n = 41

The middle term is given by 

 

⇒ a21 = a + (n – 1) d

= 12 + (21 – 1) × 6

= 12+ 20 ×6 

= 132

Answer 2

Middle term is 132  in  AP where first term is 12, the common difference is 6 if the last term of AP is 252

Given:

• An AP
• The first term is 12
• The common difference is 6
• The last term   is 252

To Find:

• Middle Term

Solution:

• Arithmetic sequence (AP)
• Sequence of terms in which difference between one term and the next is a constant.
• This is also called Arithmetic Progression AP
• Arithmetic sequence can be represented in the form :
• a, a + d  , a + 2d , …………………………, a + (n-1)d
• a = First term
• d = common difference = aₙ-aₙ₋₁
• nth term =  aₙ =  a + (n-1)d

In Given AP

a = 12

d = 6

last term = 252

Step 1:

Calculate the number of terms

aₙ =  a + (n-1)d

=> 252 =12 + (n - 1)6

=> 240 = (n - 1)6

=> 40 = n- 1

=> n = 41

Step 2:

Find Middle term

middle term is (41 + 1)/2 = 21st term

a₂₁ = a + (21 - 1)d

a₂₁ = 12 + 20 (6)

a₂₁ = 132

Hence Middle term is 132