Question

please hell with 13, 14, 15, 16, 17

13. Use the binomial theorem to expand: (w-11) 14. Use mathematical induction to prove the following: 3+ 7 + 11 + 15 + ... + (4n-1) = n(2n+1) 15. Write an expression for the n" term of the sequence 2! 3! 4! 5! 6! 7! 4'5'6'7'8'9' 16. The sixth term of an arithmetic sequence is 20.6, and the ninth term is 30.2. a. Find the nth term b. Find the 20 term 17. The area of a triangle can be determined from the following Matrix. Using that matrix find the area of a triangle with points at (-2,3), (1,5), and (4,1) Area It |xz Yz 1

Answer 1

Given a B (1- ا) ....... هاته + نه، د ماه :"(a + b) +راج کرد + اسا + کلاسی - - ا) کرد ه 104انه + دو گانه چی + رحابها 10 + رده ۱۰ د ۱ امید (اگرسیار :. کے دس دن + هدایای. . . را دهة 23+ 3315) + خه ۱۰ء) + ادا کک + کا) * داده + 24/25 و هم د Given - put na ni nt term is ده () * ا+ (-) ۱۴۱

☺ Given an= c+61-1) d.. . 062a+61) d.. . a +5d=.2016. 20. ans a+6–1d. ausd = 30.2 -0, solving 0:46 .. i ...: atsd - 2016 atgd 30L : -30 29.6 do 3.27 a: 2016-5/3-2) E 20°6.-160 @=46 an= a + (n-1)d = 14.6+ (-1) 21 Oro =. 4-6+. (20~1)(3-4). 5 406 +19(3.4 = 46.460.5

Given. i :. (2, 4) = {2,3) (82.)) = (lis) (23643). V.). di Yul: Area = II Area -II) Air Yu). . *.393.11 1 2 3 IES =441=2(8-)-3(1-4) +1(1-2) - + +[=204)-3(-3) +1(-19) =+*(-879-19] 2¢¢[-18) - . [-] VEFS