Question

If an AP consists of n terms with 1st term 'a' and nth term 'l' , show that the sum of the mth term from the beginning and the mth term from the end is (a + l) .

Answer 1

Answer:

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here is your answer!!!!!!!1

Here, mth term from last = (n-m+1)th term from begining.

Now Sum of mth term from begining and mth term from last

= am + an-m+1

= a + (m - 1)d + a + (n - m + 1 - 1)d

= 2a + (m - 1 +n - m)d

= a + a + (n - 1)d

= a + an

= a + L

hope it helps !!!!!!!

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Answer 2

Answer:

Given: First term of the AP = a

Given : Last term of the AP = 1.

Given : Total number of terms = n.

Common difference from the beginning=d

Common difference from the end = -d.

.. Last term of the AP = nth term of the AP

» an = |

» a + (n - 1) * d = 1

Now,

→nth term of the AP from the beginning an = a + (n - 1) * d

→ nth term from the end = 1 + (n - 1) * (-d)

= 1 - (n - 1) * d

Sum of nth term from the beginning + nth term from the end is given by:

→a + (n - 1) * d + [1 - (n - 1) * d]

→ a + (n - 1) * d+1- (n - 1) * d

→ a + nd - d +1- nd + d

→a + l