Question

find the sum of all even numbers from 4 to 134​

Answer 1

Even numbers from 4 to 134:

4, 6, 8, ... , 132, 134

Here:

• First term = a = 4
• Common Difference = d = 6 - 4 = 2
• Last term = aₙ = 134

Sₙ = n/2 [2a + (n - 1)d]

This can also be written as:

Sₙ = n ÷ 2 [a + (a + (n - 1)d] → → → {Equation 1}

We know that:

aₙ = a + (n - 1)d → → → {Equation 2}

⇒ 134 = 4 + (n - 1)2

⇒ 134 = 4 + 2n - 2

⇒ 134 = 2n + 2

⇒ 2n = 134 - 2

⇒ 2n = 132

⇒ n = 132 ÷ 2

∴ n = 66

Using value of an of Equation 2 in Equation 1;

Sₙ = n ÷ 2 (a + aₙ)

Substituting the values,

⇒ Sₙ = 66 ÷ 2 (4 + 134)

⇒ Sₙ = 33 (138)

∴ Sₙ = 4554

Hence, Sum of all even numbers from 4 to 134 is 4554.

Answer 2

I hope this will help you