Question

Find the number of the terms in an ap ....7,13,19.....205

Answer 1

Answer :

n = 34

Step-by-step explanation :

   $\underline{\underline{\bf Arithmetic \ Progression(AP):}}$

• It is the sequence of numbers such that the difference between any two successive numbers is constant.

• In AP,

       a - first term

       d - common difference

       n - number of terms

        l - last term

      aₙ - nth term

      Sₙ - sum of n terms

• General form of AP,

       a , a+d , a+2d , a+3d , ..........

• Formulae :-

        nth term of AP,

          $\boxed{\bf a_n=a+(n-1)d}$

        Sum of n terms in AP,

          $\boxed{\bf S_n=\frac{n}{2}[2a+(n-1)d]}$

          $\boxed{\bf S_n=\frac{n}{2}[a+l]}$

_____________________________

Given AP,

 7 , 13 , 19, ....., 205

first term, a = 7

common difference, d = 19 - 13 = 13 - 7 = 6

last term, l = 205

let last term be the nth term,

   aₙ = 205

we know,

      $\boxed{\bf a_n=a+(n-1)d}$

Substitute the values,

      205 = 7 + (n - 1) (6)

      205 = 7 + 6n - 6

      205 = 1 + 6n

        6n = 205 - 1

        6n = 204

          n = 204/6

          n = 34

Therefore, The number of terms = 34