Question

Solve the equation : 1+4+7+10+.…..............+x=287.

Answer 1

Given, 1 + 4 + 7 + 10 +...+ x = 287

This series in AP.

Now, first term a = 1

common difference d = 4 - 1 = 3

Last term l = x

Let number of terms = n

Now, Sum of the seires Sn = 287

=> (n/2)*{2a + (n - 1)d} = 287

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

=> (n/2)*{2 + 3n - 3} = 287

=> (n/2)*{3n - 1} = 287

=> n*(3n - 1) = 287*2

=> 3n2 - n = 574

=> 3n2 - n - 574 = 0

=> (n - 14)*(3n + 41) = 0

=> n = 14, -41/3

Since n can not be nagtive,

So, n = 14

i.e. there are 14 terms in the series and x is the 14th term.

So, x = a14 = a + (14 - 1)d

=> x = a + 13d

=> x = 1 + 13*3

=> x = 1 + 39

=> x = 40

So, the value of x is 40