The sum of the 3rd and the 7th term of an A.P. is 30 and the sum of the 5th…
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The sum of the 3rd and the 7th term of an A.P. is 30 and the sum of the 5th and the 9th term is 56. Find the sum of the 4th and the 8th terms of the same series
Answer: B. 43 — Let the first term be a and the common difference be d. Write the given sums in terms of a and d: a3 + a7 = (a + 2d) + (a + 6d) = 2a + 8d = 30. a5 + a9 = (a +…
- A.
46
- B.
43
- C.
38
- D.
29
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Correct answer: B
Let the first term be a and the common difference be d.
Write the given sums in terms of a and d:
a3 + a7 = (a + 2d) + (a + 6d) = 2a + 8d = 30.
a5 + a9 = (a + 4d) + (a + 8d) = 2a + 12d = 56.
Subtract the first equation from the second to eliminate a:
(2a + 12d) - (2a + 8d) = 56 - 30 ⇒ 4d = 26 ⇒ d = 6.5.
Substitute d = 6.5 into 2a + 8d = 30 to find a:
2a + 8(6.5) = 30 ⇒ 2a + 52 = 30 ⇒ 2a = -22 ⇒ a = -11.
Compute the required sum a4 + a8:
a4 + a8 = (a + 3d) + (a + 7d) = 2a + 10d.
Plugging in a = -11 and d = 6.5 gives 2(-11) + 10(6.5) = -22 + 65 = 43.
Therefore the sum of the 4th and 8th terms is 43.