Question

the sum third and fourth terms of an ap is 6 and their product is 8 find the sum of first 16 terms ​

Answer 1

Answer:

Step-by-step explanation:

The third and seventh term of the ap can be written as a+2d and a+6d respectively.

a+2d +a+6d = 6

2a + 8d = 6

a+4d = 3 So, a = 3-4d

Now, (a+2d)(a+6d) = 8 (given)

we can also write as , (3-4d + 2d)(3-4d+6d) = 8 (a=3-4d as derived above)

(3-2d)(3+2d) = 8

9-4d2 = 8

4d2= 1

d = 1/2

Now we have to find the sixteenth term, i.e a+15d

a = 3-4d and d=1/2

So, a=3-4x1/2

a = 1

a+15d = 1 + 15x1/2 = 17/2