Question

One term of an arithmetic sequence is 45 and its common difference is 8. Can the sum of any 15 terms be 2020? Why?​

Answer 1

Given :  one term of an arithmetic sequence is 45 and its common difference is 8

To find : Can sum of any 15 terms be 2020 ?

Solution:

One term  is  45

Common difference  =  8  

any term can be of form  45  +  8k

where k is integer ( negative & positive both )

Now sum of any term will be of  form

15 * 45   + 15 * 8 * k

=  675 + 120 * k

120 * k  will always end with 0

& 675 ens with 5

Hence their sum will end with  5

5 - 0 = 5  & 5 + 0 = 5

Hence 675 + 120 * k  ≠ 2020

Hence sum of any 15 terms can not be 2020

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