Question

the sum of the 4th and 8th terms of an arithmetic progression is 24 and the sum of the 6th and 10th terms is 44.find the first three terms of the arithmetic progression​

Answer 1

Step-by-step explanation:

according to the question

a4 + a8 =24

then a+3d+a+7d=24

2a+10d=24

2a=24-10d --------------1

also a6 + a10=44

which means

a+5d+a+9d=44

2a+14d=44

using 1 (2a= 10d-24)

24-10d+14d=44

4d=20

d=5

then you can easily find a

and 5 terms you can find with help of a and d

Answer 2

Answer:

First three terms of the A.P. are: -13, -8, -3

Step-by-step explanation:

Tn = a + (n-1)d

Where:

Tn = nth Term

a = First Term

n = Term Position

d = Common Difference

T4 = a + (4-1)d

T4 = a + 3d — (i)

T8 = a + (8-1)d

T8 = a + 7d — (ii)

T6 = a + (6-1)d

T6= a + 5d — (iii)

T10 = a + (10-1)d

T10 = a + 9d — (iv)

A.T.Q:

T4 + T8 = 24

Putting values of T4 & T8 from (i) & (ii)

a + 3d + a + 7d = 24

2a + 10d = 24

2a = 24 - 10d — (v)

T6 + T10 = 44

Putting values of T6 & T10 from (iii) & (iv)

a + 5d + a + 9d = 44

2a + 14d = 44 — (vi)

Putting value of 2a from (v) into (vi)

24 - 10d + 14d = 44

4d = 44 - 24

4d = 20

d = 5

Putting value of d into (v)

2a = 24 - 10X5

2a = 24 - 50

2a = -26

a = -13

General equation for A.P series: a, a+d, a+2d....

Putting a & n in the general equation to find first 3 terms:

-13, -13 + 5, -13 + 2X5

-13, -8, -13 + 10

-13, -8, -3

So, first three terms of the A.P. are: -13, -8, -3