Question

Solve for x . 1+4+7+10+....+x=247 ​

Answer 1

Series is 1+4+7+.....+x

which is in A.P. where

First term, a=1

and Common difference, d=a2−a1=4−1=3

Let total no. of terms is n

Sum of n terms, Sn=287

Sn=2n{2a+(n−1)d}

So,

2n{2(1)+(n−1)3}=287

n{2+3n−3}=574

3n2−n=574

3n2−n−574=0

3n2−42n+41n−574=0

n=14  or  n=−341

n cannot be negative so n=14

Now x is the nth term.

x=a+(n−1)d

=1+13(3)=40

Answer 2

Answer:

see the attachment for the solution

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now,