If 1+5+7+10+......+x = 287 find the value of x

1.	If 1+5+7+10+......+x = 287 find the value of x
Answer» Given, 1 + 4 + 7 + 10 +...+ x = 287This series in AP.Now, first term a = 1, common difference d = 4 - 1 = 3Last term l = xLet number of terms = nNow, Sum of the seires Sn = 287=> (n/2) ×{2a + (n - 1)d} = 287=> (n/2) ×{2 + (n - 1)3} = 287=> (n/2) ×{2 + 3n - 3} = 287=> (n/2) ×{3n - 1} = 287=> n ×(3n - 1) = 287 ×2=> 3n2 - n = 574=> 3n2 - n - 574 = 0=> (n - 14) ×(3n + 41) = 0=> n = 14, -41/3Since n can not be negative,So, n = 14i.e. there are 14 terms in the series and x is the 14th term.So, x = a14 = a + (14 - 1)d=> x = a + 13d=> x = 1 + 13 ×3=> x = 1 + 39=> x = 40So, the value of x is 40

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