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

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

- 270
- 735
- 1409
- 1470

**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.