Question

Solve the equation: 1+4+7+10+...+x=2871+4+7+10+...+x=287

Answer 1

Answer:

Here, a = 1,

and d = 4 - 1 = 2,

S(n) = n

Let n be the number of terms.

We know that,

S(n) = n/2[2a + (n - 1)d]

Putting all the values, we get

⇒ 287 = n/2[2 × 1 + (n - 1) (3)]

⇒ 287 = n/2[2 + (n - 1)3]

⇒ 574 = 3n² - n

⇒ 3n² - n - 574 = 0

⇒ 3n² - 42n + 41n - 574 = 0

⇒ 3n(n - 14) + 41(n - 14) = 0

⇒ n = 14, - 41/3 (As n can't be negative)

⇒ n = 14

We know that,

a + (n - 1)d = x

⇒ 1 + (14 - 1) (3) = 3

⇒ 1 + 13 (3) = 3

⇒ x = 40.