Question

Find the first terms and common difference of an A.P. whose t8=3 and
t12=52.​

Answer 1

Answer:

a+(8-1)d = 3

a+(12-1)d = 52

7d = 3

11d = 52

-4d = -49

d = 49/4

a+7×49/4= 3

a+343/4 = 3

a = 12-343/4

a = -331/4

Answer 2

Answer:

-331/4

Explanation:

Given:

t8 = 3 & t 12 = 52

To find:

The first term  and common difference  

Solution:

The formula of the nth term of an A.P. is as follows:

 

where  

= last term, t = first term, n = no. of terms and d = common difference

We have,

∴  

. . . . Equation 1

and

∴  

. . . . Equation 2

On subtracting equation 2 from equation 1, we get

t + 11d = 52

t + 7d = 3

-  -         -

--------------------

 4d = 49

-------------------

∴ d = 49 / 4

On substituting the value of d = 49 / 4 in equation 1, we get

 

Thus,