Question

please solve it its urgent.

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Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{ \therefore \text{8,13,21,34,55,89,144,233,377,610}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline{ \bold{Given : }}} \\ \implies series = a,b,(a + b),(a + 2b) \\ \: \: \: \: \: \: \: \: \: \: \: (2a + 3b).(3a + 5b),(5a + 8b) \\ \: \: \: \: \: \: \: \: \: \: (8a + 13b),(13a + 21b),(21a + 34b) \\ \\ \bold{Where : } \\ \circ \: a = 8 \\ \circ \: b = 13 \\ \\ \red{\underline{ \bold{ To \: Find: }}} \\ \implies 10 \: fibonacci \: numbers = ?$

• According to given question :

$\text{ Putting \: values \: of \: a \: and \: b}\\ \implies First \: number = a = 8 \\ \\ \implies Second \: number = b = 13\\ \\ \implies 8 + 13 = 21 \\ \\ \implies 13 + 21 = 34\\ \\ \implies 21 + 34 = 55\\ \\ \implies 34 + 55 = 89 \\ \\ \implies 55 + 89 = 144 \\ \\ \implies 89 + 144 = 233 \\ \\ \implies 144 + 233 = 377 \\ \\ \implies 233 + 377 = 610 \\ \\ \therefore \text{numbers \: are} \\ \green{\implies \text{8,13,21,34,55,89,144,233,377,610}} \\ \\ \blue{\text{fibonacci \: numbers : }} \\ \implies \text{A \: series \: of \: numbers \: in \: which } \\ \: \: \: \: \: \: \: \: \: \text{sum \: of \: two \: preceding \: numbers \:} \\ \: \: \: \: \: \: \: \: \: \text{is \: equal \: to \: next \: number }$

• For verifcation :

$\bold{Verfication : } \\ \implies Sum \: of \:all \: numbers = 11 \times 7th \: number \\ \\ \implies 8 + 13 + 21 + 34 + 55 + 89 + \\ \: \: \: \: \: \: \: \: \: \: 144 + 233 + 377 + 610 = 11 \times 1584 = (5a + 8b) \\ \\ \implies 1584= 11 \times (40 + 104) \\ \\ \implies 1584 = 11 \times 144 \\ \\ \implies 1584 = 1584 \\ \: \: \: \: \: \: \: \green{\huge\text{Verified}}$

Answer 2

{ \bold{given : }}} \\ \implies series = a.b.(a + b).(a + 2b) \\ \: \: \: \: \: \: \: \: \: \: \: (2a + 3b).(3a + 5b).(5a + 8b) \\ \: \: \: \: \: \: \: \: \: \: (8a + 13b).(13a + 21b).(21a + 34b) \\ \\ \bold{where : } \\ \circ \: a = 8 \\ \circ \: b = 13 \\ \\ \red{\underline{ \bold{ to \: find: }}} \\ \implies 10 \: fibonacci \: numbers = ?[/tex]

• According to given question :

[tex] \text{ putting \: values \: of \: a \: and \: b}\\ \implies first \: number = a = 8 \\ \\ \implies second \: number = b = 13\\ \\ \implies 8 + 13 = 21 \\ \\ \implies 13 + 21 = 34\\ \\ \implies 21 + 34 = 55\\ \\ \implies 34 + 55 = 89 \\ \\ \implies 55 + 89 = 144 \\ \\ \implies 89 + 144 = 233 \\ \\ \implies 144 + 233 = 377 \\ \\ \implies 233 + 377 = 610