Arithmetic Sequence Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

An arithmetic sequence has

a_1 = 7

and

d = -3

. Find

a_{20}

and

S_{20}

1
Use the arithmetic sequence formula to find the 20th term: $a_n = a_1 + (n-1)d$ , where $a_1 = 7$ , $d = -3$ , $n = 20$ .
2
Calculate: $a_{20} = 7 + (20-1)(-3) = 7 - 57 = -50$
3
Apply the partial sum formula: $S_{20} = \frac{20}{2}(a_1 + a_{20}) = 10(7 + (-50)) = 10(-43) = -430$

Answer

a_{20} = -50

;

S_{20} = -430

With a negative common difference the sequence decreases. The sum formula averages the first and last terms and multiplies by the count.

About Arithmetic Sequence

A sequence where each term is obtained from the previous by adding a fixed constant called the common difference $d$ .

In an arithmetic sequence [formula] and [formula]. Find [formula] and [formula].

Find the 15th term of [formula]

Find the sum of all integers from 1 to 100.

Find the sum of the first 20 terms of the arithmetic sequence: 5, 8, 11, 14, ...