Question

5 The fifth term of an AP is 26 and its tenth term is 51. Find ap​

Answer 1

Step-by-step explanation:

Given:-

The fifth term of an AP is 26 and its tenth term is 51.

To find:-

Find the AP ?

Solution:-

Let the First term of an AP = a

Let the Common difference = d

Let the Number of terms = n

We know that

The General or nth term of an AP

= an = a+(n-1)d

Now given that

The fifth term of an AP = 26

=> a 5 = 26

=> a+(5-1)d = 26

a+4d = 26 --------------------(1)

and

tenth term of the AP = 51

=> a 10 =51

=> a+(10-1)d = 51

a+9d = 51 ---------------(2)

On subtracting (1) from (2)

=> (2) - (1)

a+9d = 51

a+4d = 26

(-)

___________

0+5d = 25

___________

=> 5d = 25

=> d = 25/5

=> d = 5

On Substituting the value of d in (1) then

=> a+4(5) = 26

=> a +20 = 26

=> a = 26-20

=> a = 6

First term of the AP = 6

Common difference = 5

The general form of an AP = a, a+d,a+2d,...

a= 6

a+d = 6+5 = 11

a+2d = 6+2(5)=6+10=16

The AP : 6,11,16,21,26,...

Answer:-

The Arithmetic Progression for the given problem is 6, 11 , 16 , 21, 26, ...

Check:-

5th term = 6+4(5)=6+20=26

10th term=6+9(5)=6+45=51

Verified the given relations

Used formulae:-

1.The general form of an AP = a, a+d,a+2d,...

2.The General or nth term of an AP = an = a+(n-1)d

3.The First term of an AP = a

The Common difference = d

The Number of terms = n

Answer 2

Answer:

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