Add the numbers in the series 3+11+19+27 + ... + 395+403.

Sum = 10,232

Step-by-step explanation:

The given sequence is Arithmetic Progression.

Arithmetic Progression is a sequence in which every two neighbor digits have equal distances.

For finding the sum of given series firstly we find the number of terms in given series.

For finding the nth term, we use formula

aₙ = a + (n - 1) d

where, aₙ = value of nth term

a = First term

n = number of term

d = difference

Now, In given sequence: 3+11+19+27 + ... + 395+403

a = 3, d = 8, aₙ = 403

∴ 403 = 3 + (n - 1) * 8

⇒ n = 51

Now, the sum of series is determined by formula,

Sₙ = n : 2 [ a + l]

where l = last term

⇒ Sₙ = 51 : 2 [ 3 + 403]

⇒ Sₙ = 51 * 203

⇒ Sₙ = 10,232