0 Rajan@2021Guru Asked: March 16, 20212021-03-16T09:02:04+05:30 2021-03-16T09:02:04+05:30In: ICSE Solve the equation : 1+4+7+10+…+x=287 0 An important question from ML Aggarwal(avichal Publication). We have been asked to find the value of X. Solve the equation : 1+4+7+10+…+x=287 Arithmetic Progression, Chapter 9, Question no 6 arithmetic progressionclass 10ml aggarwal Share Facebook 1 Answer Voted Oldest Recent MathsMentor Guru 2021-03-16T19:12:00+05:30Added an answer on March 16, 2021 at 7:12 pm Here,givena=1 d=4−1=3 and,sn=287 Now, sn=2n(2a+(n−1)d) ⇒287=2n(2×1+(n−1)3) ⇒287=2n(2+3n−3) ⇒574=n(3n−1) ⇒574=3n2−n⇒3n2−n−574=0 on solving the quadratic equaton using formula n=2a−b±b2−4ac We get n=14 & 3−41[does not exist] so, n=14 Now, sn=2n(a+1) ⇒287=214(1+x) ⇒574=14(1+x) ⇒(1+x)=14574⇒1+x=41 ⇒x=41−1 ∴x=40 x=40 is the solution. 0 Reply Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp Leave an answerLeave an answerCancel reply Featured image Select file Browse Add a Video to describe the problem better. Video type Youtube Vimeo Dailymotion Facebook Choose from here the video type. Video ID Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs". Click on image to update the captcha. Save my name, email, and website in this browser for the next time I comment. Related Questions Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back ... Find the values of k for which the pair of linear equations kx + 3y = k-2 and ... . Solve for x and y: 0.4x-1.5y = 6.5, 0.3x-0.2y=0.9. Solve graphically the system of linear equations 4x-5y +16=0 and 2x+y-6 = 0. Determine the vertices of the ... If the remainder on division of x3 + 2x2 + kx +3 by x – 3 is 21, ...

## Here,givena=1

## d=4−1=3

## and,sn=287

## Now,

## sn=2n(2a+(n−1)d)

## ⇒287=2n(2×1+(n−1)3)

## ⇒287=2n(2+3n−3)

## ⇒574=n(3n−1)

## ⇒574=3n2−n⇒3n2−n−574=0

## on solving the quadratic equaton using formula n=2a−b±b2−4ac

## We get n=14 & 3−41[does not exist] so, n=14

## Now,

## sn=2n(a+1)

## ⇒287=214(1+x)

## ⇒574=14(1+x)

## ⇒(1+x)=14574⇒1+x=41

## ⇒x=41−1

## ∴x=40

## x=40 is the solution.