Question

1 +4+7+10+.....……+x=287. find the value of x​

Answer 1

Answer:

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Solution :-

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.

Hence, the value of x is 40.

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Answer 2

Sn = n/2(2a+(n-1)d) given a=1, d=4-1=3 & Sn = 287

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

287*2 = n(2 + 3n - 3)

574 = 2n + 3n^2 - 3n

3n^2 -n - 574 = 0

on solving the quadratic equation using formula n= -b + sq.root(b^2 -4ac)

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2a

we get n = 14, -41/3 n not equal to -41/3 due to negative nos.

n=14

Sn = n/2 (a +l)

287 = 14/2(1 +x)

574 = 14 (1+x)

574 / 14 = 1+x

41 = 1 + x

So, x = 41 - 1

x = 40 is the solution