Question

the sum of the first 7terms of ap is 140 and the sum of the next 7terms of the same progression is 385 then find the ap​

Answer 1

Answer:

Given, a1+a2+a3+a4+a5+a6+a7 = 140

=> a+(a+d)+(a+2d)+(a+3d)+(a+4d)+(a+5d)+(a+6d)=140

=> 7a + 21d = 140

=> a + 3d = 20 -----------------------(1)

a8+a9+a10+a11+a12+a13+a14 = 385

=> (a+7d)+(a+8d)+(a+9d)+(a+10d)+(a+11d)+(a+12d)+(a+13d) = 385

=> 7a + 70d = 385

=> a + 10d = 55 --------------------(2)

now, subtract (1) from (2) we get

7d = 35

=> d = 5

put this value in equation (1) we get

a = 5

=>AP: 5, 10, 15, ......