Question

In an Ap the first term is 5 and the common difference is 2 .If the last term of the Ap is 53 , find its middle term.

Answer 1

the middle term is 25th term

Answer 2

Answer:

The Middle term of AP is 29

Step-by-step explanation:

• AP is the progression in which the difference between the 2 consecutive terms is constant.
• The nth term of AP is given as

       $a_{n} =a+(n-1)d$   where a is the first term and d is a common

     difference.

Step 1 of 1:

• First-term of AP =5
• Common difference=2
• Last term of AP =53
• The number of terms is given by

       $a_{n} =a+(n-1)d$

       $53 =5+(n-1)2\\53-5=(n-1)2\\48=(n-1)2\\24=n-1\\n=25$

• The Middle term of AP is  $\frac{25+1}{2} =13$
• The 13th term of AP is given by

          $a_{n} =a+(n-1)d$

            $a_{13} =5+(13-1)2\\a_{13}=5+12(2)\\a_{13}=5+24\\a_{13}=29$