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  • The first term of an AP is 3, the last term is 83 and the sum of all its terms in 903. Find the number of terms and the common difference of the AP.      

The first term of an AP is 3, the last term is 83 and the sum of all its terms in 903. Find the number of terms and the common difference of the AP.

 

 

 

Answers (1)

Given

            First Term    a = 3

            Last Term    a_n = 83 = l

            Sum of n terms    S_n = 903

    \begin{align*}S_n& = \frac{n}{2}[a + l]\\ 903 & = \frac{n}{2} [ 3 + 83] \\ 903 &= \frac{n}{2}\times 86\\\Rightarrow n & = 21\end{align*}

       \begin{align*} a_n &= a + (n-1)d \\ 83 &= 3 + 20d \\ \Rightarrow d & = 4\end{align*}             

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Safeer PP

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