Question

Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

Factors and multiples
ANSWERED
asked 2021-08-02
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

Answers (1)

2021-08-03
Step 1 Given W.K.T.
Multiples of 2 as well as of \(\displaystyle{5}={L}{C}{M}\) os (2,5)
\(\displaystyle={10}\)
Step 2 Finding the sum
Multiples of 2 as well as of 5 between 1 and \(\displaystyle{500}={10},{20},{30},\ldots,{490}\)
\(\displaystyle{a}_{{{1}}}={10}\)
\(\displaystyle{a}_{{{2}}}={20}\)
\(\displaystyle{d}={a}_{{{2}}}-{a}_{{{2}}}\)
\(\displaystyle={20}-{10}\)
Let
The number of terms in this \(\displaystyle{A}{P}={n}\)
\(\displaystyle{a}_{{{n}}}={a}+{\left({n}-{1}\right)}{d}\)
\(\displaystyle{490}={10}+{\left({n}-{1}\right)}{10}\)
\(\displaystyle{480}={\left({n}-{1}\right)}{10}\)
\(\displaystyle{n}-{1}={48}\)
\(\displaystyle{n}={49}\)
Sum of an AP
\(\displaystyle{S}_{{{n}}}={\frac{{{n}}}{{{2}}}}{\left[{a}+{1}\right]}\)
\(\displaystyle={\frac{{{49}}}{{{2}}}}{\left[{10}+{490}\right]}\)
\(\displaystyle={49}\times{250}\)
\(\displaystyle={12250}\)
Sum of those integers between 1 and 500 which are multiples of 2 as well as of \(\displaystyle{5}={12250}\)
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...