Question

Find the sum of the arithmetic sequence. 17, 19, 21, 23, ..., 35 (1 point)

Answer 1

260

Explanation:

Given the first and last terms in the sequence , calculate the sum using

`S_(n)` =
`(n)/(2)` (a + l)

where a is the first term and l the last term

Here a = 17 and l = 35

To calculate the number of terms use the n th term formula

`a_(n)` = a + (n - 1)d

where d is the common difference

a = 17 and d = 19 - 17 = 2 and
`a_(n)` = 35, thus

17 + 2(n - 1) = 35 ( subtract 17 from both sides )

2(n - 1) = 18 ( divide both sides by 2 )

n - 1 = 9 ( add 1 to both sides )

n = 10

Hence

`S_(10)` = 5(17 + 35) = 5 × 52 = 260

Answer 2

260

Explanation:

a= 17

common difference (d ) = 19-17 = 2

a+(n-1)d = 35

17+(n-1)2 = 35

(n-1)2 = 35-17

n-1 = 18/2

n-1= 9

n = 9+1 = 10

Sum of the arithmetic sequence

= n/2[2a+(n-1)d]

= 10/2 [ 2(17)+ (10-1)2]

= 5(34+18)

= 5× 52

=260