Search Colleges, Courses, Exams, Questions and Articles

Ask a query on 8879100846 Ask Login | Sign Up

 

 

› Ask & Answer › Question

79. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

0 2 Views | Posted 4 months ago
Asked by Shiksha User

  • 1 Answer

  • P

    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    79. An A.P. of numbers from 1 to 100 divisible by 2 is

    2, 4, 6, ……….98, 100.

    So, a = 2 and d = 4-2 = 2

    l= 100

    ⇒a+(n−1)d=100

    ⇒2+(n−1)2=100

    ⇒22+(n−1)22=1002

    ⇒1+(n−1)=50

    ⇒n=50

    Let, s1=2+4+6?+9+100=502[2+100]{?Sn=n2(a+1)}

    =50×1022

    = 2550

    Similarly, an A.P. of numbers from 1 to 100 divisible by 5 is

    5,10,15, ……. 95,100

    So, a = 5 and d = 100

    l= 100

    ⇒a+(n−1)d=100

    ⇒5+(n−1)5=100

    ⇒1+(n−1)=20

    ⇒n=20

    ∴S2=5+10+15…+95+100=202[5+100]

    =20×1052

    = 1050

    As there are also no divisible by both 2 and 5 , i.e., LCM of 2 and 5 = 10 An A.P. of no. from 1 to 100 divisible by 10 is 10, 20, …………100

    So, a = 10, d = 10

    l=100

    ⇒a+(x−1)l=100

    ⇒10+(x−1)10=100

    ⇒1+(x−1)=10

    ⇒x=10

    So, S3=10+20+30+…+100=102[10+100]

    = 550

    The required sum of number =S1+S2S3=2550+1050−550=3050

    = 3050

Similar Questions for you

1In an increasing arithmetic progression a1, a2,....an if a5 = 2 and product of a1, a5 and a4 is greatest, then the value of dis equal to
A
alok kumar singh

First term = a

Common difference = d

Given: a + 5d = 2        . (1)

Product (P) = (a1a5a4) = a (a + 4d) (a + 3d)

Using (1)

P = (2 – 5d) (2 – d) (2 – 2d)

-> = (2 – 5d) (2 –d) (– 2) + (2 – 5d) (2 – 2d) (– 1) + (– 5) (2 – d) (2 – 2d)

d P d d = –2 [ (d – 2) (5d – 2) + (d – 1) (5d – 2) + (d – 1) (5d – 2) + 5 (d – 1) (d – 2)]

= –2 [15d2 – 34d + 16]

d = 8 5   o r   2 3

at  ( 8 5 ) , product attains maxima

-> d = 1.6

In a 64 terms GP if sum of total terms is seven times sum of odd terms, then common ratio is
A
alok kumar singh

a, ar, ar2, ….ar63

a+ar+ar2 +….+ar63 = 7 [a + ar2 + ar4 +.+ar62]

a ( 1 − r 6 4 ) ( 1 − r ) = 7 a ( 1 − r 6 4 ) ( 1 − r 2 )            

1 + r = 7

r = 6

In an arithmetic progression if sum of 20 terms is 790 and sum of 10 terms is 145, then S15 – S5 is (when Sn denotes sum of n terms)
A
alok kumar singh

S20 = 2 0 2 [2a + 19d] = 790

2a + 19d = 79              . (1)

S 1 0 1 0 2 [ 2 a + 9 d ] = 1 4 5

2a + 9d = 29                . (2)

from (1) and (2) a = –8, d = 5

S 1 5 − S 5 = 1 5 2 [ 2 a + 1 4 d ] − 5 2 [ 2 a + 4 d ]

= 1 5 2 [ − 1 6 + 7 0 ] − 5 2 [ − 1 6 + 2 0 ]  

= 405 – 10

= 395

If 3, 7, 11,...., 403 = AP1

2, 5, 8, ...., 401 = AP2

Find sum of common term of AP1 and AP2
A
alok kumar singh

3, 7, 11, 15, 19, 23, 27, . 403 = AP1

2, 5, 8, 11, 14, 17, 20, 23, . 401 = AP2

so common terms A.P.

11, 23, 35, ., 395

->395 = 11 + (n – 1) 12

->395 – 11 = 12 (n – 1)

3 8 4 1 2 = n − 1    

32 = n – 1

n = 33

Sum =  3 3 2 [2×11+ (32)12]

=  3 3 2 [22 + 384]

= 6699

If 3, a, b, c are in A.P. and 3, a – 1, b + 1 are in G.P. Then arithmetic mean of a, b and c is
A
alok kumar singh

3, a, b, c are in A.P.

a – 3 = b – a                                                 (common diff.)

2a = b + 3

and 3, a – 1, b + 1 are in G.P.

a − 1 3 = b + 1 a − 1              

a2 + 1 – 2a = 3b + 3

a2 – 8a + 7 = 0                         &n

...more

Get authentic answers from experts, students and alumni that you won't find anywhere else

Sign Up on Shiksha

On Shiksha, get access to

  • 65k Colleges
  • 1.2k Exams
  • 688k Reviews
  • 1800k Answers

Learn more about...

Share Your College Life Experience

Write a Review

Didn't find the answer you were looking for?

Search from Shiksha's 1 lakh+ Topics

or

Ask Current Students, Alumni & our Experts

Ask Now
Community GuidelinesUser Points System
QuestionsDiscussionsTags
×
×

This website uses Cookies and related technologies for the site to function correctly and securely, improve & personalise your browsing experience, analyse traffic, and support our marketing efforts and serve the Core Purpose. By continuing to browse the site, you agree to Privacy Policy and Cookie Policy.

Need guidance on career and education? Ask our experts

Characters 0/140

The Answer must contain atleast 20 characters.

Add more details

Characters 0/300

The Answer must contain atleast 20 characters.

Keep it short & simple. Type complete word. Avoid abusive language. Next

Your Question

Edit

Add relevant tags to get quick responses. Cancel Post