Find The nth Term of an A.P. is (3+n)/4 :

The nth term of an A.P. is (3+n)/4, then the sum of first 105 terms is

  1. 270
  2. 735
  3. 1409
  4. 1470
Anurag Mishra Professor Asked on 30th September 2015 in Maths.
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1 Answer(s)

Answer: (4) 1470

Explanation:-

The nth term of an A. P. = (3 + n)/4
Then, the first term of A. P. = (3 + 1)/4 = 4/4 = 1
The second term of A. P. = (3 + 2)/4 = 5/4
The third term pf A. P. = (3 + 3)/4 = 6/4 = 3/2
Then, d = 3/2 – 5/4 = (6 – 5)/4 = 1/4

Formula-
The sum of the first n terms of an A. P. = (n/2) [2 a + (n – 1) d]

Where , a = first number or first term

Then, the sum of the first 105 terms = (105/2) [ 2 x 1 + (105 – 1) x 1/4]
= (105/2) [2 + 104/4]
= 105/2 [2 + 26]
= 105 x 28/2
= 105 x 14
= 1470

Then, the sum of first 105 terms is 1470.

Hence, the answer is (4) 1470.

Anurag Mishra Professor Answered on 3rd October 2015.
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