NIMCET 2013 — Mathematics PYQ

Solution

To find the sum, we first identify the sequence of multiples of 7 between 200 and 400.

Step 1: Find the first and last terms

• Dividing 200 by 7: $200÷7=28$ with a remainder of 4. The first multiple after 200 is $7\times 29=203$.

• Dividing 400 by 7: $400÷7=57$ with a remainder of 1. The last multiple before 400 is $400-1=399$.

So, the sequence is: 203, 210, 217, ..., 399.

This is an Arithmetic Progression (AP) where:

• First term ($a$) = $203$

• Last term ($l$) = $399$

• Common difference ($d$) = $7$

Step 2: Find the number of terms ($n$)

Using the formula for the $n^{th}$ term:

Step 3: Find the sum of the sequence ($S_n$)

Using the sum formula for an AP:

Final Answer: The sum is 8729.