ts polycet 2021 | Solved Previous Question Papers 2021 Maths

 Given AP is 2, – 1, – 4 ……

     First term (మొదటి పదం) = a =2

 Common difference (సామాన్య భేదం) =d =   – 1 – 2 = – 3 

 10^th term (పదవ పదం) = a₁₀ = a + 9d

                                   = 2 + 9(– 3)

                                    = 2 – 27 = – 25

 Two-digit numbers divisible by 7 are: 14, 21, 28, …… ,98

 14, 21, 28, …… ,98 in AP

    a = 14, d = 7 and a_n= 98

   a_n= 98

 ⟹ a + (n – 1) d = 98

  14 + (n – 1) (7) = 98

  (n – 1) (7) = 98 – 14

       = 84

  n – 1 = 84/7 = 12

   n = 13       

Given AP is 3, 6, 9, ….

     a= 3, d = 6 – 3 = 3 and n = 15

we know that sum of n terms of AP = S_n =

  ∴ The sum of 15 terms of AP 3, 6, 9…. is 360

 Given ∑n = 45

 We know that sum of n natural numbers

= 1 + 2 + …. + n = ∑n =

  మొదటి n సహజ సంఖ్యల మొత్తం = ∑n =

  ⟹  = 45

  n(n + 1) = 90

 n² + n = 90

  n² + n – 90 = 0

  n² + 10n – 9n – 90 = 0

  n (n +10) – 9(n+ 10) = 0

 (n + 10) (n – 9) = 0

 n= – 10 or n = 9

 ∴ n = 9 (∵ number of terms cannot be negative)