Question

the middle term of an arithmetic progression having (2n+1) term is m. show that the sum of its (2n+1) terms is (2n+1)m​

Answer 1

Answer:

S(2n + 1) = (2n + 1)m.

Step-by-step explanation:

(2n + 1) is Odd

Therefore, Middle term is = t (2n + 1 - 1)/2

Therefore, t (n + 1) = m

Let , t1 = a c.d. = d [d not equals to 0]

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

m = (a + nd)

Now ,

S (2n + 1) = (2n + 1)/2 [2a + (2n + 1 - 1) d]

= (2n + 1)/2 [2a + 2nd]

= (2n + 1)/2 × 2 (a + nd)

= (2n + 1) × (a + nd)

= (2n + 1)m

[PROVED]

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