Question

Question 18 The sum of 4 th and 8 th terms of an A.P. is 24 and the sum of the 6 th and 10 th terms is 44. Find the first three terms of the A.P.

Class 10 - Math - Arithmetic Progressions Page 107

Answer 1

A/C to question,
T₄ + T₈ = 24 __________(1)
and T₆ + T₁₀ = 44 ____________(2)
Let a is the first term and d is the common difference of AP
then,
a + 3d + a + 7d = 24
2a + 10d = 24
a + 5d = 12 _______(1)

a + 5d + a + 9d = 44
2a + 14d = 44
a + 7d = 22________(2)

solve eqns (1) and (2)
2d = 10 , d = 5 and a = -13

hence, -13 , -8, - 3 ...........

Answer 2

General term or nth term of A.P The general term or nth term of A.P is given by an = a + (n – 1)d, where a is the first term, d is the common difference and n is the number of term. ______________________________________________________________ Solution:

Given:
a4 + a8= 24
a6+a10= 44

Let a be the first term and d the common difference of an AP.

We know that,
an = a + (n − 1) d

a4 = a + (4 − 1) d
a4 = a + 3d

Similarly,
a8 = a + 7d
a6 = a + 5d
a10 = a + 9d

a4 + a8 = 24. ( given)
a + 3d + a + 7d = 24
2a + 10d = 24
a + 5d = 12 … (i)

a6 + a10 = 44. (Given)
a + 5d + a + 9d = 44
2a + 14d = 44
a + 7d = 22 … (ii)

On subtracting equation (i) from (ii)
2d = 22 − 12
2d = 10
d = 5

From equation (i), we get
a + 5d = 12
a + 5 (5) = 12
a + 25 = 12

a = −13

a2 = a + d = − 13 + 5 = −8
a3 = a2 + d = − 8 + 5 = −3

Hence, the first three terms of this A.P. are −13, −8, and −3.

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Hope this will help you.