Question

The third term of an arithmetic sequence is 15 and when 20 is added to the third term the

8 term is obtained
a) What is the common difference of the sequence?
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b) What is the position of 103 in this sequence?​

Answer 1

Common difference = 4

Position of 103 = 25th term

Explanation:

a)

According to the given information:

`a_3 + 20 = a_8`

`a+ (3-1)d + 20 = a+ (8-1)d`

`\cancel a+ 2d + 20 = \cancel a + 7d`

`2d + 20 = 7d`

`20 = 7d-2d`

`20 = 5d`

`d = (20)/(5)`

`\purple {\bold {d = 4}}`

Common difference = 4

b)

`\because a_3 = 15....(given)`

`\therefore a + (3-1)d = 15`

`\therefore a + 2d = 15`

`\therefore a + 2* 4= 15`

`\therefore a + 8= 15`

`\therefore a = 15-8`

`\red{\bold {\therefore a = 7}}`

`\because a_n = a + (n - 1) d`

`\therefore 103 = 7 + (n - 1)4`

`\therefore 103 - 7 = (n - 1)4`

`\therefore 96 = (n - 1)4`

`\therefore (96)/(4)= n - 1`

`\therefore 24= n - 1`

`\therefore 24+1= n`

`\blue{\bold {\therefore n = 25}}`

So, the position of 103 in this sequence is 25th term.