Question

The sum of the 4th and 8th terms of an APis 24 and the sum of the 6th and 10th terms is 44.Find three terms of the AP​

Answer 1

Answer:

a+3d+a+7d=24  

2a+10d=24

2(a+5d)=24

a+5d=12         --------1

a+5d+a+9d=44

2a+14d=44

2(a+7d)=44

a+7d=22      ---------2

subtract both equations

a+5d-(a+7d)=12-22

a+5d-a-7d=-10

-2d=-10

d=5

put this value of d in 1

a+5*5=12

a+25=12

a=12-25

a=-13

first three terms=a=-13

                           a+ d=-13+5=-8

                           a+2d=-13+2*5+-13+10=-3

SO THE FIRST THREE TERMS ARE= -13,-8,-3

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Answer 2

here is your answer

a+3d+a+7d=24  

2a+10d=24

2(a+5d)=24

a+5d=12        equation  --------1

a+5d+a+9d=44

2a+14d=44

2(a+7d)=44

a+7d=22      equation ---------2

subtract both equations

a+5d-(a+7d)=12-22

a+5d-a-7d=-10

-2d=-10

d=5

put this value of d in 1

a+5*5=12

a+25=12

a=12-25

a=-13

first three terms=a=-13

                          a+ d=-13+5=-8

                          a+2d=-13+2*5+-13+10=-3

ap formed= -13,-8,-3

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--extra information

Notation in AP

In AP, we will come across three main terms, which are denoted as:

• Common difference (d)

• nth Term (an)

• Sum of the first n terms (Sn)

All three terms represent the property of Arithmetic Progression.  

Common Difference in Arithmetic Progression

1. In this progression, for a given series, the terms used are the first term, the common difference between the two terms and nth term. Suppose, a1, a2, a3, ……………., an is an AP, then; the common difference “ d ” can be obtained as;

d = a2 – a1 = a3 – a2 = ……. = an – an – 1

Where “d” is a common difference. It can be positive, negative or zero.

First Term of AP

The AP can also be written in terms of common difference, as follows;

a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d

where  “a” is the first term of the progression

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