Question 18
The sum of $4^{t h}$ and $8^{t h}$ terms of an A.P. is 24 and the sum of the $6^{t h}$ and $10^{t h}$ terms is 44. Find the first three terms of the A.P.

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Solution

We know that,
$a_{n} = a + (n - 1) d a_{4} = a + (4 - 1) d a_{4} = a + 3 d S i m i l a r l y, a_{8} = a + 7 d a_{6} = a + 5 d a_{10} = a + 9 d G i v e n t h a t, a_{4} + a_{8} = 24 a + 3 d + a + 7 d = 24 a + 5 d = 12 \dots (i) a_{6} + a_{10} = 44 a + 5 d + a + 9 d = 44 2 a + 14 d = 44$
a+7d=22 .....(ii)
On subtracting equation (i) from (ii), we get,
2d = 22 - 12
2d = 10
d = 5
From equation (i), we get
a + 5d = 12
a + 5 (5) = 12
a + 25 = 12
a = −13
$a_{2} = a + d = - 13 + 5 = - 8$
$a_{3} = a_{2} + d = - 8 + 5 = - 3$
Therefore, the first three terms of this A.P. are −13, −8, and −3.

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Similar questions

4^{t h}

8^{t h}

6^{t h}

10^{t h}

The sum of the $4^{th}$ and $8^{th}$ term of an A.P is $24$ and the sum of its $6^{th}$ and $10^{th}$ terms is $44$ . Find the first term?

4^{t h}

8^{t h}

24

6^{t h}

10^{t h}

34

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