Question

The fifth term of an AP is 52 and its twelfth term is 24. find AP Class X​

Answer 1

            Solution        

It is given here that :-  fifth term of an AP is 52 and its twelfth term is 24

We know that a(n) = a +(n-1) d

So,

Fifth Term a(5) = a + (5-1)d

$\implies$ 52 = a+4d $\longrightarrow$(1)

Also,

Twelfth Term a(12) = a + ( 12 - 1) d

$\implies$ 24 = a + 11d $\longrightarrow$ (2)

Now, let us subtract (1) from (2)

              a    +   11d   =  24

             (-)a +(-) 4d  = (-)52          

                       7d      = -28

7d = -28

$\sf d = \dfrac{-28}{7} = -4$

$\bigstar$ Common Difference (d) = -4

Now substituting value of d as -4 in (1)

a + ( 4 × -4 ) = 52

a + -16 = 52

a = 52 + 16 = 68

$\bigstar$ First Term (a) = 68

We know that the general format of an AP is a,a+d,a+2d,a+3d , .... a+nd

Here, Since

a = 68 and d = -4

The AP will become  68 , 68 + (-4) , 68 + 2(-4) , 68 + 3(-4) , 68 + 4(-4)

$\red\bigstar$ So, The AP is 68 , 64 , 60 , 56 , 52,.....