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Question 842166: The sum of the 4th and 8th term of an AS sequence is 24 whilst the sum of the 15th and 19th term of the sequence is 68 determine the 5th term
Answer by TheInstructor(29)   (Show Source):
You can put this solution on YOUR website! I love Series and Sequences questions!
Okay so your sum of T4 + T8 = 24
Now remember what is T4 equal to? a+3d
T8 = a+7d
So a+3d + a+7d = 24
Therefore: 2a+10d = 24
T15 + T19 = 68
T15 = a+14d
T19 = a+ 18d
Therefore: (a+14d)+ (a+18d) = 68
This means: 2a+ 32d = 68
So we have two equations. Now we can solve them simultaneously!
2a+ 32d = 68 ------------ (2)
2a+ 10d = 24 ------------ (1)
So (2) - (1): 22d = 44
Therefore: d = 2
If your d = 2; You can sub this into any of your previous equations to find a
2(a) + 32(2) = 68
2a = 4
Therefore a =2
Now using Tn = a+(n-1)d formula, we can find the 5th term yay!
T5 = 2+(5-1).2 = 10
Therefore your 5th term would be 10!
(Added info: T4 = 8, T8 = 16) (T15 = 30, T19 = 38)
Hope that helped! Stay awesome! :)
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