Let’s observe the addition sums given below carefully.
15 + 16 + 17 + 18 + 19 + 20 + 21 (Odd number of consecutive terms)
32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 (Even number of consecutive terms)
Look at both the expressions. First expression consists of consecutive terms but the number of terms are 7, which is an odd number. It means there are odd number of consecutive terms. Whereas, in case of second expression, there are even number (10 terms) of consecutive terms.
Important point to be kept in mind is whether the consecutive terms are odd or even in number. Accordingly the formula will be used. Let’s look at the formula below.
For odd number of consecutive terms
Multiply the middle term by the number of terms.
Example 1:- 15 + 16 + 17 + 18 + 19 + 20 + 21 = ?
Solution:- Multiply 18 (middle term) by 7 (number of terms)
Ans. 18 × 7 = 126
Example 2:- 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 = ?
Solution:- Multiply 31 (middle term) by 9 (number of terms)
Ans. 31 × 9 = 279
Note:- If the middle term is an even number, the sum will be always even. Whereas if the middle term is an odd number, the sum will be odd.
For even number of consecutive terms
Multiply the mean of the two middle terms by the number of terms.
Example 1:- 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 = ?
Solution:- Find the mean of the two middle terms. 36 + 37/ 2 = 73/2 = 36.5
Multiply 36.5 (mean) by 10 (number of terms). 36.5 × 10 = 365
Ans. 365
Example 2:- 45 + 46 + 47 + 48 + 49 + 50 + 51 + 52 = ?
Solution:- Find the mean of two middle terms. 48 + 49 / 2 = 97/2 = 48.5
Multiply 48.5 (mean) by 8 (number of terms). 48.5 × 8 = 388
Ans. 388
Note:- In case of even number of consecutive terms, the mean will be always .5 greater than the first middle term or .5 lesser than the second middle term.
HAPPY LEARNING………………….