Question

If there are 10 terms of the sequence {2, 7, 12, 17, ...}, what is its mean?​

Answer 1

24.5

Explanation:

The mean is calculated as

mean =
`(sum)/(count)`

The consecutive terms in the sequence have a common difference d

d = 7 - 2 = 12 - 7 = 17 - 12 = 5

This indicates the sequence is arithmetic with sum to n terms

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 5 , thus

`S_(10)` =
`(10)/(2)` [ (2 × 2) + (9 × 5) ]

= 5(4 + 45)

= 5 × 49 = 245 , then

mean =
`(245)/(10)` = 24.5