Question

3, 8, 13, ......,373 are in arithmetic series. The sum of numbers not divisible by three is

• A. 9310
• B. 8340
• C. 9525
• D. 7325

Answer 1

The Correct Option is C

Given Arithmetic Progression: 3, 8, 13, ..., 373

Step 1: Finding the number of terms (n):

T_n = a + (n - 1)d

Substitute \( T_n = 373, a = 3, d = 5 \):

373 = 3 + (n - 1)5

\( 370 = 5(n - 1) \)

\( n - 1 = \frac{370}{5} = 74 \)

\( n = 75 \)

Step 2: Sum of the arithmetic progression:

\(\text{Sum} = \frac{n}{2} [a + l]\)

Substitute \( n = 75, a = 3, l = 373 \):

\(\text{Sum} = \frac{75}{2} [3 + 373] = \frac{75}{2} (376) = 75 \cdot 188 = 14100\)

Step 3: Finding the sum of terms divisible by 3: Numbers divisible by 3 are 3, 18, 33, ..., 363.

\( 363 = 3 + (k - 1)15 \)

\( 360 = (k - 1)15 \)

\( k - 1 = \frac{360}{15} = 24 \)

\( k = 25 \)

Sum of these terms:

\(\text{Sum} = \frac{k}{2} [a + l]\)

Substitute \( k = 25, a = 3, l = 363 \):

\(\text{Sum} = \frac{25}{2} [3 + 363] = \frac{25}{2} (366) = 25 \cdot 183 = 4575\)

Step 4: Required sum:

\(\text{Required Sum} = 14100 - 4575 = 9525\)