Let \(S(n)\) equal the sum of the digits of positive integer \(n\). For example, \(S(1507)=13\) . For a particular positive integer \(n\), \(S(n)=1274\). Which of the following could be the value of \(S(n+1)\)?

I'm getting 1239 as an answer.

Please help!

tertre
Mar 14, 2018

#1**0 **

n is an integer..... n+1 is the NEXT sequential integer.....obtained by adding '1' to the n integer....so the sum of the digits COULD be '1' greater. Is this a multiple choice question? What are your choices?

1275

ElectricPavlov
Mar 14, 2018

#3**0 **

The question asks what 'could' the next one be.....and we weren't given any multiple choices...

ElectricPavlov
Mar 14, 2018

#4**+1 **

We are looking for an integer whose sum of its digits = 1274

Here's a possibility :

S(n) = 1274 = S ( 7777....7) where we have 7 repeated 182 times

Note that 7 * 182 = 1274

So.... S ( n + 1) = S( [7777....7] + 1 ) = S(1275) = S (555.....5) where we have 5 repeated 255 times

Note that 255 * 5 = 1275

CPhill
Mar 14, 2018

#5**0 **

We are talking about a VERY large number here....there are thousands of possibilities....without knowing the starting a1 and the r of the series and where in the series you are, it could be almost anything.....were you given any more information...or multiple choices?

ElectricPavlov
Mar 15, 2018