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It is an arithmetic series.

a = -4 d = +3

-4 - 1 + 2 + 5 + .... + (x-3) + x = 437

Sum of the series = [ 2 a + (n-1)d ]n /2 = 437

[ - 8 + 3(n-1) ] n / 2 = 437

- 11n + 3n² = 874

3 n² -11n - 874 = 0

n = (11 +- 103 )/6 = 114/6 = 19 as n is +ve only.

So x = a + (n-1)d = -4 + 3 (19-1) = 50

a = -4 d = +3

-4 - 1 + 2 + 5 + .... + (x-3) + x = 437

Sum of the series = [ 2 a + (n-1)d ]n /2 = 437

[ - 8 + 3(n-1) ] n / 2 = 437

- 11n + 3n² = 874

3 n² -11n - 874 = 0

n = (11 +- 103 )/6 = 114/6 = 19 as n is +ve only.

So x = a + (n-1)d = -4 + 3 (19-1) = 50

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

First term(a) = - 4

common difference(d) = 3

- 4 - 1 + 2 + 5 + .... + x = 437

so now using formula for sum of n terms

⇒437= n/2[ -8 + (n-1)3]

⇒n[ -8 + 3(n-1) ] = 874

⇒ -11x=n + 3n² = 874

⇒3n² -11n - 874 = 0

Using sidharacharya

no. of terms cannot be negative the we take the positive value

n = 19

So

x = a + (n-1)d = -4 + 3 (19-1) = 50

common difference(d) = 3

- 4 - 1 + 2 + 5 + .... + x = 437

so now using formula for sum of n terms

⇒437= n/2[ -8 + (n-1)3]

⇒n[ -8 + 3(n-1) ] = 874

⇒ -11x=n + 3n² = 874

⇒3n² -11n - 874 = 0

Using sidharacharya

no. of terms cannot be negative the we take the positive value

n = 19

So

x = a + (n-1)d = -4 + 3 (19-1) = 50