Question

Find the sum of the arithmetic sequence if a1 = 1 d=-4 n =20.

Answer 1

Step-by-step explanation:

an = a + (n-1) d

= 1+(20-1) (-4)

=1+19(-4)

=1-76

= - 75

Sn= n/2(a+ an)

=20/2 {1+ (-75)}

=10 (-74)

= - 740 answer

Answer 2

Given:

The first term of an arithmetic sequence is 1, The common difference is -4 and the number of terms is 20.

To Find:

The sum of the arithmetic sequence.

Solution:

The given problem can be solved by using the concepts of arithmetic progressions.

1. It is given that the first term is 1, the common difference is -4 and the number of terms is 20.

• a1 = 1, d = -4, n = 20. (a1 implies the first term in the progression).

2. According to the Properties of an arithmetic progression, the sum of an A.P with first term a, common difference d, and n number of terms is given by:

• Sum of n terms of an A.P =$\frac{n}{2} * ( 2a + (n-1) d)$.

3. On substituting the terms in the given formula we get,

=> Sum of n terms =$\frac{20}{2}*(2*1 + (20-1) (-4)$,

=> Sum = 10*(2 + (-76)),

=> Sum = 10 * ( -74),

=> Sum = -740.  

Therefore, The sum of the first 20 terms of the arithmetic sequence is -740.