Question

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

Answer 1

let the no. be x

so, according to the questions

1+4+7+10+x+x=287

22+2x=287

2x=287-22

2x=265

x=265/2

Answer 2

Here, 1, 4, 7, 10,.......,x, is an A.P.

• First term, a = 1

• Common difference, d = 3.

☯ Let there be n terms in the A.P. Then,

⠀⠀⠀⠀⠀⠀➯ x = nth term

⠀⠀⠀⠀⠀⠀➯ x = 1 + (n - 1) × 3

⠀⠀⠀⠀⠀⠀➯ x = 1 + 3n - 3

⠀⠀⠀⠀⠀⠀➯ x = 3n - 2⠀⠀⠀⠀⠀⠀⠀eq. (1)

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━

Now,

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

➯ n/2(1 + x) = 287

➯ n/2(1 + (3n - 2)) = 287

➯ n/2(3n - 1) = 287

➯ n(3n - 1) = 287 × 2

➯ 3n² - n = 574

➯ 3n² - n - 574 = 0

➯ 3n² - 42n + 41n - 574 = 0

➯ 3n(n - 14) + 41(n - 24) = 0

➯ (n - 14)(3n + 41) = 0

➯ n = 14 or -41/3

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━

☯ Since, Number of terms can't be a fraction or negative.

Therefore,

• n = 14

★ Now, Putting value of n in eq (1),

we get,

x = 3 × 14 - 2 = 40

∴ Therefore, the sum of 40 terms is 287.