Question

The first term of an AP is 10, the last term is 50 and the sum is 400. the number of terms and the common differenee.​

Answer 1

Correct Question :

The first term of an AP is 10, the last term is 50 and the sum is 480. the number of terms and the common difference.

Answer :

• number of terms = 16
• common difference = 8/3

Step-by-step explanation :

  $\underline{\underline{\bf Arithmetic \ Progression :}}$

• 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

     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,

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

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Given,

• first term, a = 10
• last term, l = 50
• Sum = 480

To find,

• number of terms, n = ?
• common difference, d = ?

=> Sum of n terms = 480

           $S_n=\frac{n}{2}[a+l]} \\\\ 480=\frac{n}{2}[10+50] \\\\ 480=\frac{n}{2}[60] \\\\ 480 =n\times 30 \\\\ n=48/3 \\\\ n=16$

∴ The number of terms = 16

=> last term, l = 50

   

      $a_n=a+(n-1)d \\\\ 50=10+(16-1)d \\\\ 50-10=15d \\\\ 40=15d \\\\ d=40/15 \\\\ \bf d=8/3$

∴ Common difference, d = 8/3