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Question

If the nth term of an is $$(2n+1)$$,find the sum of the first n terms of the AP.


Solution

$$a_n=2n+1$$
$$a_1=2+1=3$$
$$a_2=2\cdot2+1=5$$

$$d=a_2-a_1$$$$=5-3=2$$

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

$$=\dfrac { n }{ 2 }[6+(n-1)2]$$

$$=\dfrac {n }{ 2 }[2n+4]$$  

Maths

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