Question

If sum of an A.P 1, 4, 7, 10,...,x is 287 then find the value of x.​

Answer 1

Answer:

x=40

Step-by-step explanation:

1, 4, 7, 10,...,x

a=1,d=4-1=3

let the sum of  n terms=287

287=n/2( 2*1+(n-1)*3)

2*287=n( 2+3n-3)

574=3n²-n

3n²-n-574=0

n={ 1 ±√(1+4*3*574}/6

=(1 ±√6889)/6

=34±83)/6

Rejecting negative vlaue

n=(1+83)/=54/6=14

Hence x is 14th term

x=1+13*3

=1+39=40

x=40