SOLUTION: 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

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! :)
RELATED QUESTIONS
If the 4th term of an arithmetic sequence is 31 and the 8th term of the sequence is 59,... (answered by ewatrrr)

In an arithmetic sequence the 8th term is twice the 4th term and the 20th term is 40.... (answered by mananth)

Find the 10th term of an arithmetic sequence whose 5th term is 1.25 and whose 15th term... (answered by ikleyn)

Find the 10th term of an arithmetic sequence whose 5th term is 1.25 and whose 15th term... (answered by Fombitz)

What is the 15th term of the arithmetic sequence with a1 =10 and d=... (answered by ewatrrr)

the 15th term in an arithmetic sequence is 129 and the sum of the first fifteen terms is... (answered by josgarithmetic,greenestamps)

If 15th and 11th term of an A.P are 3 and 23 respectively. Is 40 the term of the sequence (answered by stanbon)

What is the sum of the first 50 terms of the arithmetic sequence in which the 3rd term is (answered by ikleyn)

the third term of an arithmetic sequence is 34 and the 15th term is -14. Determine the... (answered by stanbon)