Find the sum of the following:

3 + 11 + 19 + … + 803

The arithmetic progression 3, 11, 19, …., 803 is given.
Here first term is 3 and common difference is 11 – 3 = 8.
Last term l = 803

Let no. of terms be n.
So, a_n = a + (n - 1)d

Where,

a = First term of AP
d = Common difference of AP
and no of terms is ‘n’

⇒ 803 = 3 + (n - 1) × 8
⇒ 800 = (n - 1) × 8
⇒ 100 = n – 1
⇒ n = 101

Since the sum of n terms is
S_{n =}

Where,

a = First term of AP
d = Common difference of AP
and no of terms is ‘n’

So sum of 101 terms S₁₀₁
]
= 50.5[ 6 + 100×(8)]
= 50.5[ 6 + 800]
= 50.5 × (806)
= 40703

Hence, Sum is 40703.