Question

sum of first 7 terms of an ap is 182 it its fourth and the 17th term are in the ratio 1 is to 5 find the AP

Answer 1

Answer:

Step-by-step explanation:

nth term is 2+(n-1)8

Answer 2

According to the Question

$\bf\huge S_{7} = 182$

$\bf\huge\frac{a_{4}}{a_{17}} = \frac{1}{5}$

Now

$\bf\huge\frac{7}{2}[2a + 6d] = 182$

a + 3d = 26 …. (1)

$\bf\huge\frac{a_{4}}{a_{17}} = \frac{a + 3d}{a + 16d} = \frac{1}{5}$

5a + 15d = a + 16d

5a - a = 16d - 15d

4a = d ….. (2)

From (1) and (2) we get :-

a + 12a = 26

a = 2

d = 4(2)

d = 8

Therefore AP are 2, 10, 18, 26 …….