Question

the sun of three term of AP is 36 and third term is 14 ,then the commander difference is​

Answer 1

Answer:

2

Step-by-step explanation:

Given ,

Sum of three terms of an A.P(S₃) = 36

Third term(a₃) = 14

To Find :-

Common difference(d)

How To Do :-

As they gave the value of sum of '3' terms of an A.P we need to equate that value to the formula of sum of 'n' terms of an A.P . After equating we can find the value of first term(a)  and we need to substitute the value of the first term (a) in the formula of  third term of an A.P . Because they given the value of the third term of an A.P

Formula Required :-

Sum of 'n' terms of an A.P :-

$S_n=\dfrac{n}{2}[a+l]$

'n' th term of an A.P :-

$a_n=a+(n-1)d$

Solution :-

$S_3=36$

$\dfrac{3}{2}[a+14]=36$

$3[a+14]=2\times 36$

3[a + 14] = 72

3(a) + 3(14) = 72

3a + 42 = 72

3a = 72 - 42

3a = 30

a = 30/3

a = 10

∴ First term = a = 10.

a₃ = 14

a + (3 - 1)d = 14

10 + (2)d = 14

10 + 2d = 14

2d = 14 - 10

2d = 4

d = 4/2

d = 2

∴ Common difference = d = 2.