Q. 55.0( 1 Vote )

Find the sum of the first 40 terms of the series 12 – 22 + 32 – 42 + … .

Answer :

Let the sum of n terms be,


Sn= 12 –22 +32 –42+52 –62+72 –82 ….


= (12 –22) + (32 –42) + (52 –62) + (72–82) …..


= (1–4) + (9–16) + (25–36) + (49–64)……..


= –3 –7 –11 –15………………. [No. of terms ]


This represents an A.P.


(NOTE: Here the number of terms has been halved. If n= no. of terms in original series and m= no. of terms in new A.P. then )


Now, here a= –3, d= (–7 – (–3)) = –4


Sum of m terms =


=


=


=


=


=


As n= 40,


Required sum =


= –820


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