atics for Class 10
2. Find the sum of each of the following arithmetic series:
(i) 7+ 10
+103 + 14 + ... + 84.
(ii) 34 +32 +30 + ... + 10.
(iii) (-5)+(-8) + (-11)+...+(-230)
Answers
Step-by-step explanation:
ii) 34 + 32 + 30 + ………. + 10 a = 34, d = 32 – 34 =-2, an = 10, Sn =? a + (n – 1)d = an 34 + (n – 1)(-2) = 10 34 – 2n + 2 = 10 -2n + 36 = 10 -2n = 10 – 36 -2n = -26 2n = 26 = 13 × 22 ∴ S23 = 286
iii) 5 + (-8) + (-11) +……… + (-230) a = -5, d = -8 – (-5) = -8 + 5 a, = -230. Sn =? d = -3 a+(n – 1)d = an -5 + (n – 1)(-3) = -230 -5 – 3n + 3 = -230 -3n – 2 = -230 -3n = -230 +2 -3n = -228 3n = 228 ∴ n = 228/3 ∴ n = 76. = 38 × -235 ∴ S76= -8930.
i))Here last term is given i.e 84 and first term(a)=7 and common difference(d) = second term- first term = 10(1/2)- 7= 7/2 now first we need to find total number of terms to find sum. i.e n therefore last term(l) = a+(n-1)d 84=7+(n-1)7/2 84-7= (n-1)7/2 77*2/7= (n-1) 22= n-1 n= 22+1 n=23 so total term is 23 now put all values in formula to get sum sum= n/2(a+l) 23/2(7+84) 23/2*91= 1046.5 or 1046(1/2)