Q. 14.2( 217 Votes )

Find the sum of the following APs:

(i) 2, 7, 12, . . ., to 10 terms.

(ii) –37, –33, –29, . . ., to 12 terms.

(iii) 0.6, 1.7, 2.8, . . ., to 100 terms.

(iv) 1/15 , 1/12 , 1/10 , ..4 , 11 3

Answer :

(i) Here, a = 2, d = 5 and n = 10


Sum of n terms can be given as follows:



S10


= 5(4 + 45)


= 5


= 245


Thus, sum of the 10 terms of given AP (Sn)=245


(ii) Here, a = - 37, d = 4 and n = 12


Sum of n terms can be given as follows:



S12


= 6(-74 + 44)


= 6


=-180


Thus, sum of the 12 terms of given AP (Sn)= -180


(iii) Here, a = 0.6, d = 1.1 and n = 100


Sum of n terms can be given as follows:



S100


= 50(1.2 + 108.9)


= 50


=5505


Thus, sum of the 100 terms of given AP (S100) = 5505


(iv) Here,


a= , n = 11,


d =


Sum of n terms can be given as follows:



S11


= (+ )


=


=


Thus, sum of the 100 terms of given AP (Sn)=

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