Question

The first term of an Arithmetic Progression is 15 and the last term is 85. If the sum of all terms is 750, what is the 6th term?​

Answer 1

Answer : 40

lets see

The sum of all terms of this Arithmetic Progression is (n/2) (a + l) = 750.

This gives us n = 15 terms.

The 15th term of this Arithmetic Progression is (a + 14d) = 85.

Substituting for a,

we get d = 5.

Therefore, the 6th term of this Arithmetic Progression is (a + 5d) = 40

Answer 2

Solution:-

Given:-

First Term = a = 15.

Sum of all Term = 750.

To Find:-

6th Term = ?

Find:-

Sn = n/2 ( a + l)

=> 750 = n/2 ( 15 + 85)

=> 750 × 2 / 100 = n

=> n = 15.

Hence,

15th Term of the A.P. is 85.

=> a 15 = a + 14d

=> 85 = 15 + 14d

=> d = 70/14

=> d = 5.

Now,

6th Term = a6 = a + 5d

=> 15 + 5*5

=> 40.

Hence,

6th Term of the A.P. is 40.