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  • Find the sum of first 24 terms of an A.P. whose nth term is given by    

Find the sum of first 24 terms of an A.P. whose nth term is given by  a_n=3+2n

 

Answers (1)

Given : a_n=3+2n

First term  (n=1)\Rightarrow a_1=3+2\times 1

                                   \Rightarrow a_1=5

Second term (n=2)\Rightarrow a_2=3+2\times 2

                                      \Rightarrow a_2=7

Third term (n=3)\Rightarrow a_3=3+2\times 3

                                   \Rightarrow a_3=9

Fourth term (n=4)\Rightarrow a_4=3+2\times 4

                                     \Rightarrow a_4=11

A.P : 5, 7, 9, 11, ...

Common difference  (d)=7-5=2

Sum of A.P 

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

For  n=24,

S_{24}=\frac{24}{2}[2\times 5+(24-1)\times 2]

        =\frac{24}{2}\times 2[5+23]=22\times 28

S_{24}=672

Posted by

Safeer PP

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