Question

sum of first 9 terms of an arithmetic sequence is 45 and sum of first 18 terms is 171. what is the sum of it's 10 to 18 terms
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Answer 1

Answer:

126

Step-by-step explanation:

Sn = n/2(a+An)

S9=9/2(2a+8d)

45*2/9=2a+8d

10=2a+8d ------(1)

Similarly,

S18 = 18/2(2a+17d)

171*2/18 = 2a+17d

19=2a+17d ------ (2)

subtract (1) from (2)

19-10= 2a-2a+17d-8d

9=9d

=> d=1

Therefore, 10 = 2a +8(1)

10-8=2a

2=2a

=> a=1

So sum of 10 to 18 terms = S18- S9

18/2[2(1) + 17(1)] - 9/2[2(1) + 8(1)]

9*(2+17) - 9/2*(2+8)

9*19-9/2*10

9*19-9*5

9(19-5)

9*14

126

Hope it Helps!

Answer 2

let the reqd sum b s'

9

explanation : if u see then sum of 1st 18 terms can b written as sum of 1st 9 terms and sum of next 9 terms ..so if u subtract them they get cancelled and what remains is the sum of next 9 terms i.e. sum of terms 10 - 18. ......