Question

18. Find the sum of first 20 terms of A.P. 5, 9, 13, using the formula.
19. Show that the equation 4x² + 3x - 5 = 0 has no real roots.​

Answer 1

Step-by-step explanation:

18. a= 5

d= 9-5 = 4

Sn = n/2 (2a+(n-1)d )

= 20/2 ( 2×5 +(20-1)4 )

= 10( 10 +76)

= 10(86)

= 860

Answer 2

QUESTION : 18

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

$\green{\tt{\therefore{s_{20}=860}}}$

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

$\green{ \underline \bold{Given:}} \\ \tt{: \implies Arithmetic \: Progressions(A.P) = 5,9,13,..} \\ \\ \tt{: \implies Total \: number \: of \: terms(n)= 20} \\ \\ \red{ \underline \bold{To \: Find:}} \\ \tt{: \implies Sum \: of \: 20th \: terms( s_{20}) =?}$

• According to given question :

$\tt{\circ \: First \: term(a) =5} \\ \\ \tt{\circ \: Common \: difference(d)=4} \\ \\ \tt{\circ \: Number \: of \: terms (n)=20} \\ \\ \bold{As \: we \: know \: that} \\ \tt{ : \implies s = \frac{n}{2} (2a +( n - 1)d)} \\ \\ \text{putting \: given \: values} \\ \tt{: \implies s_{20} = \frac{20}{2} (2 \times 5 + (20 - 1) \times 4)} \\ \\ \tt{: \implies s_{20} = 10(10 + 76)} \\ \\ \tt{: \implies s_{20} = 10 \times 86} \\ \\ \green{\tt{: \implies s_{20} = 860}}$

QUESTION : 19

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

$\green{\tt{\therefore{D>0}}}$

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

$\green{ \underline \bold{given:}} \\ \tt{: \implies 4 {x}^{2} + 3x - 5 = 0} \\ \\ \red{ \underline \bold{to \: find:}} \\ \tt{: \implies D = ?}$

• According to given question :

$\tt{: \implies {4x}^{2} + 3x - 5 = 0} \\ \\ \tt{\circ \: a = 4} \\ \\ \tt{ \circ \: b = 3} \\ \\ \tt{ \circ \: c = - 5 } \\ \\ \bold{As \: we \: know \: that} \\ \tt{: \implies D = {b}^{2} - 4ac} \\ \\ \tt{: \implies D= {3}^{2} - 4 \times 4 \times ( - 5)} \\ \\ \tt{: \implies D = 9 + 80} \\ \\ \tt{: \implies D = 89} \\ \\ \green{\tt{: \implies D > 0}}$