Advertisements
Advertisements
Question
Find the sum of all multiples of 7 lying between 500 and 900.
Solution
The multiples of 7 lying between 500 and 900 are 504, 511, 518, … , 896.
This is an A.P.
First term, a = 504
Common difference, d = 511 − 504 = 7
Last term = 896
Let there be n terms in the A.P.
`a_n=896`
`rArr a+(n+1)d=896`
`rArr 504+(n-1)xx7=896`
`rArr (n-1)xx7=896-504`
`rArr (n-1)=392/7`
`rArr n-1=56`
`rArr n=57`
We know that, `S_n=n/2(a+l)`
∴Sum of all the multiples of 7 lying between 500 and 900
`=57/2(504+896)`
`=57/2xx1400`
`=57xx700`
`=39900`
Thus, the sum of all the multiples of 7 lying between 500 and 900 is 39900.
APPEARS IN
RELATED QUESTIONS
If the mth term of an A.P. be `1/n` and nth term be `1/m`, then show that its (mn)th term is 1.
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
0.2, 0.22, 0.222, 0.2222 ….
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`sqrt2, sqrt8, sqrt18, sqrt32 ...`
For the following arithmetic progressions write the first term a and the common difference d:
−5, −1, 3, 7, ...
Show that the sequence defined by an = 5n −7 is an A.P, find its common difference.
Find the 18th term of the AP `sqrt2, 3sqrt2, 5sqrt2.....`
Find the number of all three digit natural numbers which are divisible by 9.
Which term of an A.P. 16, 11, 6, 1, ... is – 54?
The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms
Which of the following form an AP? Justify your answer.
`1/2, 1/3, 1/4, ...`
