Question

Find the sum of the first 40 terms of an A.P. whose nth term is 3-2n.

Answer 1

this is your answer.

Answer 2

Given:    

In an arithmetic progression, the value of the nth term is 3 - 2n  

To Find:    

The sum of the first 40 terms of the A.P is?  

Solution:  

1. Consider an A.P having n terms with the first term a, common difference d. The nth term of the A.P is given by the formula,    

=> nth term of an A.P = Tn = a + (n-1)d,    

2. The first term of the A.P is,

=> t1 = a = 3 - 2(1),,

=> t1 = a = 1,

=> a = 1. ( First term = 1 )

3. The value of the second term of the A.P is,

=> t2 = a + d = 3 - 2(2),

=> t2 = a + d = -1,

=> a + d = -1,

=> 1 + d = -1,

=> d = -2. ( Common difference = -2 ).

4. The sum of the first n terms of an A.P is given by the formula,

=>$S_{n} = \frac{n}{2}(2a + (n-1)d)$.

5. The sum of the first 40 terms can be calculated using the above formula,

=> Sum = (40/2) ( 2*1 + (40-1)(-1) ),

=> Sum = 20( 2 + 39(-1) ),

=> Sum = 20(-37),

=> Sum = -740.

Therefore, the sum of the first 40 terms of the given A.P is -740.