A basic and conceptual question from arithmetic progression chapter in which we are to find the sum of each of 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,………, to 11 terms.
Book – RS Aggarwal, Class 10, chapter 5C, question no 1.
(i) 2,7,12…… to 10th term
Here a=2,n=10
And d=7−2=5
Sn=n/2[2a+(n−1)d]
S10=10/2[2(2)+(10−1)5]=5(4+9×5)=245
(ii) 37,33,29,........ to 12th term
Here a=37,n=12
And d=33−37=−4
Sn=n/2[2a+(n−1)d]
S12=12/2[2(37)+(12−1)(−4]=6(74−11×4)=−180
(iii) 0.6,1.7,2.8............ to 100 term
Here a=0.6,n=100
And d=1.7−0.6=1.1
Sn=n/2[2a+(n−1)d]
S100=100/2[2(0.6)+(100−1)(1.1)]
=50(1.2−99×1.1)
=5505
(iv)151,121,101....... to 11th term
a=151, n=11
d=1/12−1/15=(5−4)/60=1/60
S11=11/2[2(1/15+(11−1)1/60)]
= 11/2(2/15+10/60)
= 11/2×9/30=33/20