Question 1016403: the 4th term of an A.P is 15 and the 9th term is 35. Find the fifteenth term? Found 2 solutions by ikleyn, MathTherapy:Answer by ikleyn(52788) (Show Source):
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the 4th term of an A.P is 15 and the 9th term is 35. Find the fifteenth term?
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Apply the formula = for the n-th term of an AP. You will have
= + = 15. (1)
= + = 35. (2)
Take the difference (2) - (1). You will have
8d - 3d = 35 - 15 ---> 5d = 20 ---> d = = 4.
Thus we just found the common difference.
Now, = = + = + = 35 + 6*4 = 35 + 24 = 59.
Answer. = 59.
4th term ------- eq (i)
9th term ------- eq (ii)
- 20 = - 5d ------ Subtracting eq (ii) from eq (i)
d, or common difference = , or 4 ------- Substituting 4 for d in eq (i) ------- Substituting 15 for n, 3 for , and 4 for d
