Question

Find the first term of the arithetic sequence in which a24=509/4 and the common difference is 7/4

Answer 1

The first term of the arithetic sequence is 87.

Explanation:

Given,

`a_(24)=(509)/(4)` and common difference,(d)
`=(7)/(4)`

Let the first term of the arithetic sequence = a

To find, the first term of the arithetic sequence = ?

We know that,

The nth term of the arithmetic sequence,

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

⇒
`a_(24)=a+(24-1)d=a+23d`

⇒
`a+23((7)/(4))=(509)/(4)`

⇒
`a=(509)/(4)-(161)/(4)`

⇒
`a=(509-161)/(4)=(348)/(4)`

⇒ a = 87

Hence, the first term of the arithetic sequence is 87.