Question

(5) The sum of first 9 terms of an arithmetic sequence and the sum of next 8 terms are equal. If its
common difference is 5.
a) How many times of the common difference will be the difference between 10th and first
terms of this sequence?
b) What is the 9th term of this sequence?
c) What is the sum of first 17 terms of this sequence?
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Answer 1

Answer:

let the 1st term be a

2nd term will be a+5

9th term =a+40

sum of 1st 9 terms= 9a+ 180 i

using s=n/2(2a+(n-1)d)

for sum of next 8 terms

10 term will.be a+45

and last terms will be a+85

sum = 8/2(2a+90 + 7*5)=

8a+ 500 ii

then solving i = ii we get

a= 320

difference of 10th and 1st term = 45

9th term=360

sum of 17 terms= (17/2)×(320*2+ 16×4)= 5984