Question

The sum of the first 7terms of an AP is 182 if itds 4th and 17th terms are in the ratio 1:5 find the AP

Answer 1

Step-by-step explanation:

let a be first term and d is common difference then

S7 = n/2( 2a+ ( n-1) d)

182 = 7 /2 ( 2a+ 6d)

182 = 7/2 *2( a+3d)

182 = 7( a+3d)

182/7 = a+3d

26 = a+3d ............EQ 1

now

A4 = a+ 3d

A17 = a+ 16 d

A4: A17 = (a+3d) : ( a+ 16d)

from equation 1

26 / (a+16d) = 1/5

a+ 16 d = 130 ........

a= 130 - 16 d.........EQ 2

put value of a from eq 2 in eq 1

130-16d + 3d = 26

130 -13 d = 26

13 d = 130-26 = 104

d = 104/13 = 8

a = 130-16d = 130- 128 = 2

so the ap is

2,10,18,26,34..........

Answer 2

Refers to attachment ♡~