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Core 2 arithmetic series help

The sum of the 5th and 10th terms of an arithmetic series is 11.5. The sum of the first 20 terms is 85. What is the first term?

I have attempted this question however my answer does not match the one in the book and I don't understand where I went wrong with this one.

Help is very much appreciated! With clear step-by-steps on how you did it as I already know the answer, I'd just like some help on getting there :colondollar:
Reply 1
Avatar for TenOfThem
TenOfThem
18
Original post by pamplemousse1
The sum of the 5th and 10th terms of an arithmetic series is 11.5. The sum of the first 20 terms is 85. What is the first term?

I have attempted this question however my answer does not match the one in the book and I don't understand where I went wrong with this one.

Help is very much appreciated! With clear step-by-steps on how you did it as I already know the answer, I'd just like some help on getting there :colondollar:


If you show your attempt I am happy to look at where you are going wrong
Reply 2
Avatar for pamplemousse1
pamplemousse1
OP
Original post by TenOfThem
If you show your attempt I am happy to look at where you are going wrong


Thank you!

(a+4d)+(a+9d) = 11.5
2a+13d = 11.5


0.5n(2a+(n-1)d)


10x(2a+20d-d) = 85


2a+19d = 8.5


2a+13d=11.5
2a+19d=8.5


6d= -3
d= -3/6 = -0.5

13 x -0.5 = -6.5
11.5 + 6.5 = 18

2a = 18

a = 9
Reply 3
Avatar for TenOfThem
TenOfThem
18
Original post by pamplemousse1
Thank you!

(a+4d)+(a+9d) = 11.5
2a+13d = 11.5


0.5n(2a+(n-1)d)


10x(2a+20d-d) = 85


2a+19d = 8.5


2a+13d=11.5
2a+19d=8.5


6d= -3
d= -3/6 = -0.5

13 x -0.5 = -6.5
11.5 + 6.5 = 18

2a = 18

a = 9



That looks fine, what do you think the answers should be?

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