What is the sum of the of what is the sum of the given arithmetic series? 5 + 8 + 11 + ... + 92
O 1554
O 1545
O 1455
O None of these

3rd option : 1455

Step-by-step explanation:

here, a = 5, d = 3 , tn = 92, n = ?, Sn = ?

tn = [a + (n - 1) d]

92 = [ 5 + (n - 1)d

92 = 5 + 3n - 3

92 - 5 + 3 = 3n

90 = 3n

n = 90/3

n = 30

By sum of first n terms of an A. P formula,

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

Sn = 30/2 [ 2 * 5 + (30 - 1) 3]

Sn = 15[ 10 + 29 ( 3) ]

Sn = 15[ 10 + 87 ]

Sn = 15( 97 )

Sn = 15 * 97

Sn = 1455

Therefore, option 3rd 1455 is correct.