
What is the greatest number of consecutive integers whose sum is 45?
Answer
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Hint: When we add the numbers from -44 to 44 we get the sum to be 0 and adding the next number 45 to it we get the sum to be 45. Hence the numbers -44 , -43 , -42 , …… , 42 , 43 , 44 , 45 form an arithmetic sequence with the common difference 1 . We need to find the number of terms in the sequence which can be obtained by using the formula .
Complete step-by-step answer:
Step 1:
We are asked to find the greatest number of consecutive integers which add up to 45
Adding the numbers from -44 to 45 we get 45
That is when we add numbers -44 , -43 , -42 , …… , 42 , 43 , 44
We get zero and adding the next number 45 we get the sum to be 45
Step 2
Now we can see that -44 , -43 , -42 , …… , 42 , 43 , 44 , 45 forms an arithmetic sequence
The common difference can be obtained by subtracting the second term from the first term
Now we need to find the number of terms in this sequence
We have a = - 44 , d = 1 , l = 45
So the number of terms is given by
. .
Where a is first term, d is common difference,l is last term of an A.P
Substituting the values we get
Therefore the greatest number of consecutive terms that sum to 45 is 90.
Note: To find the value of n we can also use the formula
Complete step-by-step answer:
Step 1:
We are asked to find the greatest number of consecutive integers which add up to 45
Adding the numbers from -44 to 45 we get 45
That is when we add numbers -44 , -43 , -42 , …… , 42 , 43 , 44
We get zero and adding the next number 45 we get the sum to be 45
Step 2
Now we can see that -44 , -43 , -42 , …… , 42 , 43 , 44 , 45 forms an arithmetic sequence
The common difference can be obtained by subtracting the second term from the first term
Now we need to find the number of terms in this sequence
We have a = - 44 , d = 1 , l = 45
So the number of terms is given by
.
Where a is first term, d is common difference,l is last term of an A.P
Substituting the values we get
Therefore the greatest number of consecutive terms that sum to 45 is 90.
Note: To find the value of n we can also use the formula
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