Question

Find the middle term of the sequence formed by all the numbers between 9 and 95 which will leave a remainder 1 when divided by 3 also find that sum of numbers on both the sides of the middle term separately

Answer 1

Answer:

52 is middle term

sum of let terms=413

sum of right terms=1043

Step-by-step explanation:

The nos which will leave a remainder 1 when divided by 3 are

=3n+1

But no is more than 9 so

taking n=3,4,5.....

a1=10,a2=13

So no are:

10,13,16,.....................94

so middle term

=(10+94)/2

=104/2

=52

Hence 52 is middle term

Now let's count number of terms

This is an AP with a=10,d=3,l=94

l=a+(n-1)d

94=10+(n-1)3

3(n-1)=84

n-1=84/3=28

n=29

Hence number of term on both side of 52 will be 14 each

Now sum of term left to 52

=14/2(10+52-3)

=7*(10+49)

=7*59=413

Now sum of term right to 52

=14/2(52+3+94)

=7*(55+94)

=7*149

=1043