समीकरण को हल कीजिए :2 + 5 + 8 + 11 + �

1.	समीकरण को हल कीजिए :2 + 5 + 8 + 11 + … + x = 345
Answer» 2 + 5 + 8 + 11 + …. + x = 345 a = 2,d = 5 – 2 = 3 तथा l = x माना श्रेणी में पदों की संख्या = n तब l = a + (n – 1)d x = 2 + (n – 1) × 3 x = 2 + 3n – 3 x = 3n – 1 या x + 1 = 3n या n = x+1/3 तथा S_n = 345 n/2(a + l) = 345 (x+1/6)(2 + x ) = 345 2x + x² + 2 + x = 345 × 6 x² + 3x + 2 = 2070 x² + 3x + 2 – 2070 = 0 x² + 3x – 2068 = 0 x² + 47x – 44x – 2068 = 0 x(x + 47) – 44(x + 47) = 0 (x + 47)(x – 44) = 0 x + 47 = 0 तथा x – 44 = 0 x = – 47 (अमान्य), x = 44 x = 44

समीकरण को हल कीजिए :2 + 5 + 8 + 11 + … + x = 345

Answer»

2 + 5 + 8 + 11 + …. + x = 345

a = 2,d = 5 – 2 = 3 तथा l = x

माना श्रेणी में पदों की संख्या = n

तब l = a + (n – 1)d

x = 2 + (n – 1) × 3

x = 2 + 3n – 3

x = 3n – 1 या x + 1 = 3n या n = x+1/3

तथा S_n = 345

n/2(a + l) = 345

(x+1/6)(2 + x ) = 345

2x + x² + 2 + x = 345 × 6

x² + 3x + 2 = 2070

x² + 3x + 2 – 2070 = 0

x² + 3x – 2068 = 0

x² + 47x – 44x – 2068 = 0

x(x + 47) – 44(x + 47) = 0

(x + 47)(x – 44) = 0

x + 47 = 0 तथा x – 44 = 0

x = – 47 (अमान्य), x = 44

x = 44