Question

Find the sum of all multiples of 13 lying between 1301 and 1700.​

Answer 1

Answer

194350

Step-by-step explanation:

here we have range from 1301 to 1700; by dividing we can easily find out that first term in this range divisible by 13 is 1313 and last term we can find out by dividing the last value (i.e. 1700 in this case) by 13 and subtracting remainder from the dividend, thus it comes out to be 1690

Now we will have,

• a(i.e. first term) = 1313
• common difference(d) = 13
• last term (L)= 1690

Now, to apply the formula of summession of series we need the number of terms lying in this range, we can easily find out that by applying formula

Nth term= a+(n-1)d

Or 1690 =1313+(n-1)13

Or 1690-1313=(n-1)13

Or 1677/13=(n-1)

Or 129 = n-1

therefore n = 130

Thus, now we have

• a(first term)= 1313
• d(common difference)= 13
• last term(L) = 1690
• & total no. of terms in this range(n)= 130

Thus we can easily apply formula

Sum of nth term= {n(a+L)}/2

Or {130(1313+1677)}/2

Or {130×2990}/2

Or 388770/2

= 194350 Answer