Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Solve the equation- 4 + (-1) + 2 +...+ x = 437

Answers (1)

$\\$Given series :$\\ -4 + (-1) + 2 + $ \ldots $ + x = 437\\ $Here a $= - 4\\ d = - 1 - (-4)\\ -1 + 4 = + 3\\ S\textsubscript{n} = 437 $ (given)$\\ $We know that $ {{S}_{n}}=\frac{n}{2}\left[ 2a+\left( n-1 \right)d \right] \\437=\frac{n}{2}[2(-4)+(n-1) 3]\\ 874 = n[- 8 + 3n - 3]\\ 874 = 3n\textsuperscript{2} - 11n\\ 3n\textsuperscript{2} - 11n - 874 = 0\\ 3n\textsuperscript{2} - 57n + 46n - 874 = 0\\ 3n (n - 19) + 46 (n - 19) = 0 \\ (n - 19) (3n + 46) = 0\\ n - 19 = 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2n + 16 = 0\\ n = 19 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: n = - 46/3\\ $Hence $n = 19 \\ a\textsubscript{n} = x \\ a + (n - 1)d = x $ (using a\textsubscript{n }$= a + (n-1)d )\\ -4 + (19 - 1)3 = x\\ -4 + (18)3 = x\\ -4 + 54 = x\\ x = 50\\$

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question