Question

The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the A.P.

Answer 1

Answer:

The AP is  2,10,18,26,.......

Step-by-step explanation:

Given :  

S7 = 182 , a4 : a17 = 1 : 5  

Now,  

a4 / a17 = 1/5  

By using the formula ,an = a + (n - 1)d

a + (4 -1)d/a + (17 - 1)d = 1/5

(a + 3d)/(a + 16d) = ⅕

5(a + 3d) = 1(a + 16d)

[By cross multiplication]

5a + 15d = a + 16d

5a - a = 16d - 15d

4a = d

d = 4a ………….. (1)

By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]

S7 = 7/2[2a + (7 - 1)d)]

182 = 7/2 [2a + 6d]

182 = 7/2 × 2[a + 3d]

182/7 = a + 3d

a + 3d = 26

a + 3(4a) = 26  

[from eq (1)]

a + 12a = 26

13a = 26

a = 26/13

a = 2

First term ,a  = 2

On putting the value of a = 2 in eq 1,

d = 4a

d = 4 × 2

d = 8

Common Difference,d = 8  

The required AP is  a , a+d , a + 2d , a,+ 3d , a + 4d ……

Hence, the AP is  2,10,18,26,.......

HOPE THIS ANSWER WILL HELP YOU…..

Answer 2

Answer:

your answer is in ATTACHMENT