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Vesna [10]
3 years ago
13

Can somebody help me with number 7? Please explain as well! :)

Mathematics
1 answer:
gayaneshka [121]3 years ago
4 0
To factor number 7 :
3x^2-12
3x^2+3×-4
3*1, -4:2*-2
3(x^2-2^2)
use difference of square formula ((a^2+b^2=(a+b)(a-b))
3(x+2)(x-2)
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Help I need it now!!<br> T14= 46, and t20= 100, find t3, t7, and tn
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Answer:

t_3 = -53\\\\\\t_7 = -17\\t_n= -80 +9n

Step-by-step explanation:

Arithmetic sequence:

       \sf \boxed{t_n=a+(n-1)d}

Here a is the first term and d is the common difference.

      t_{14}= 6    ⇒  \sf a + 13 d = 46  ------------(I)

     \sf t_{20} = 100 ⇒   a + 19d = 100 ---------(II)

Subtract equation (I) from (II)

(I1)    a + 19d = 100

(II)    a + 13d   =  46

      <u>-    -            -</u>

               6d = 54

                d = 54 ÷ 6

                 \sf \boxed{d = 9}

Substitute d = 9 in equation(I) and find 'a',

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     a + 117  = 46

              a = 46 - 117

              a = -71

         

\sf t_3 = -71 + 2*9

   = -71 + 18

   = -53

          \sf t_7 = -71 + 6*9

              = -71 + 54

              = -17

\sf t_n= -71 + (n-1)*9

    = -71 + 9*n - 1 *9

    = -71 + 9n - 9

    = -71 - 9 + 9n

     = - 80 + 9n

   

   

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