Math, asked by varkyviji, 9 months ago

one term of an arithmetic sequence is 45 and its common difference is 8. can the sum of any 15 terms be 2020?why?

Answers

Answered by amitnrw

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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