Question

Find the last digit of the number 1^3 + 2^3 + 3^3 +.......+12^3?
d
Select one:
O a. 4
b. 5
. 5
O c. 3
d. 6​

Answer 1

Answer:-

To find:

Last digit of the result of the sum 1³ + 2³ + 3³ +.... + 12³.

We know that,

Sum of cubes of n natural numbers = n²(n + 1)²/4

Also,

nth term of an AP – aₙ = a + (n - 1)d

Here,

• a = 1
• aₙ = 12
• d = 2 - 1 = 1.

So, 12 = 1 + (n - 1)(1)

⟹ 12 = 1 + n - 1

⟹ 12 = n

Hence,

Sum of cubes of first 12 natural numbers = (12)² × (12 + 1)²/4

⟹ Sum of cubes of first 12 natural numbers = 144 * 13 * 13/4

⟹ Sum of cubes of first 12 natural numbers = 6084

We observe that the last digit of the result obtained is 4. (6084)

Therefore, the required answer is 4 (Option - a).