Question

the sun of the 4th and 8th terms of an Arithetic progression is 24 and the sum of the 6th and 10th terms is 44 find first threre terms of the Arithetic progression.

Answer 1

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Answer 2

Hello


QUESTION:- the sun of the 4th and 8th terms of an Arithetic progression is 24 and the sum of the 6th and 10th terms is 44 find first threre terms of the Arithetic progression.

ANSWER:-We know that formula a+(n-1)d

Then,
Let the first term of ap=a
Difference=D

According to the question:-


n4=a+(4-1)d
n4=a+3d


Again,
n8=a+[8-1)d
n8=a+7d

So,

Sum of 4th and 8th term

a + 3d + a + 7d = 24

2a + 10d = 24

a + 5d = 12.................... (i)

Again,

n6=a+(6-1)d
n6=a+5d

Also,

n10=a+[10-1)d
n10=a+9d

then,

Sum of 6th and 10th term


a 6 + a 10 = 44

a + 5d + a + 9d = 44

2a + 14d = 44

a + 7d = 22 ......................(ii

Solving the Equation:-)

Subtracting (i) from (ii),

2a+14d-2a-10d=44-24

4d=20

d=5

Then,

Putting the value of d in eq (1)

a + 5d = 12

a + 5 (5) = 12

a + 25 = 12

a = −13


So,


Totally Answer:-) The first three terms of this A.P. are −13, −8, and −3.


that's all


@Sujeet Yaduvanshi