Question

solve the equation 1+4+7+10......+x= 286​

Answer 1

There is a mistake in the question. The correct is written below.

Question:

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

Answer:

x = 14

Step-by-step explanation:

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

From the above series, we get the following information,

• First term, a = 1
• Second term, ${\sf{a_2}}$ = 4
• Common Difference, d = ${\sf{a_2 - a}}$ = 4 - 1 = 3
• Sum of series upto 'x' terms, ${\sf{S_x}}$ = 287

${\boxed{\sf{\red{Formula \ : \ S_n = {\dfrac{n}{2}} [2a + (n - 1)d]}}}}$

Putting n = x, we get

→ ${\sf{S_x = {\dfrac{x}{2}} [2a + (x - 1)d]}}$

Putting known values, we get

→ ${\sf{287 = {\dfrac{x}{2}} [2(1) + (x - 1)(3)]}}$

→ ${\sf{287 = {\dfrac{x}{2}} [2 + (x - 1)(3)]}}$

→ ${\sf{287 = {\dfrac{x}{2}} [2 + 3x - 3]}}$

→ ${\sf{287 = {\dfrac{x}{2}} [3x - 1]}}$

→ ${\sf{287 = {\dfrac{(x)(3x - 1)}{2}}}}$

→287 × 2 = (x)(3x - 1)

→ 574 = 3x² - x

→ 3x² - x - 574 = 0

By Middle Term Factorisation, we get

→ 3x² - 42x + 41x - 574 = 0

→ 3x(x - 14) + 41(x - 14) = 0

→ (3x + 41)(x - 14) = 0

Using Zero Product Rule, we get

→ 3x + 41 = 0 and x - 14 = 0

→ x = - 41/3 and x = 14

'x' can't be negative and in fraction.

Hence, the value of x is 14.

Answer 2

Step-by-step explanation:

hope it helps you good evening