Question

The sum of 6 terms which form an AP is 345. The difference between the first and last term is 55. Find the terms.

Answer 1

I hope it is correct answer.....

Answer 2

Answer:

The terms are 30, 41, 52, 63, 74, 85.

Step-by-step explanation:

The general form A.P. is a, a+d, a+2d, a+3d, ......, a+(n-1)d.

Step 1:

But there are only six terms are there so

a, a+d, a+2d, a+3d, a+4d, a+5d.

Sum of six terms is 345.

Step 2:

So a+a+d+a+2d+a+3d+a+4d+a+5d = 345

6a + 15d = 345------------ (1)

Difference between last term and first term is 55.

(a + 5d) – (a) = 55

5d = 55

d = 11 -------------- (2)

Step 3:

6a + 15d = 345

6a + 15 (11) = 345

6a + 165 = 345

6a = 345 – 165

6a = 180

a = 30

Then,  

Step 4:

a = 30, d = 11,

So  

A.P. is 30, 41, 52, 63, 74, 85.