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

Solution:

Given, the sum of the terms up to x is 287.

We have to solve the equation.

The sum of the first n terms of an AP is given by

Sₙ = n/2[2a + (n-1)d]

Here, first term, a = 1

So, 287 = n/2[2(1) + (n - 1)3]

287 = n/2[2 + 3n - 3]

287 = n/2[3n - 1]

574 = n(3n - 1)

3n² - n = 574

3n² - n - 574 = 0

n = -b±√(b²-4ac)/2a

Here, a = 3, b = -1 and c = -574

n = -(-1)±√((-1)²-4(3)(-574))/2(3)

= 1±√(1+6888)/6

= 1±√6889/6

n = (1±83)/6

Now, n = (1+83)/6 = 84/6 = 14

n = (1-83)/6 = -82/6 = -41/3

Since a negative term is not possible, n = -41/3 is neglected.

So, n = 14

The nth term of the series in AP is given by

aₙ = a + (n - 1)d

So, x = 1 + (14 - 1)(3)

= 1 + 13(3)

= 1 + 39

= 40

Therefore, the value of x is 40.

✦ Try This: Solve the equation : 1 + 4 + 7 + 10 +...+ x =188

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.4 Sample Problem 2

Summary:

On solving the equation 1 + 4 + 7 + 10 +...+ x =287, the value of x is 40

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