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.

Step-by-step explanation:

Given,

$a_{24}=\dfrac{509}{4}$ and common difference,(d)$=\dfrac{7}{4}$

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,

$a_{n}=a+(n-1)d$

⇒ $a_{24}=a+(24-1)d=a+23d$

⇒ $a+23(\dfrac{7}{4})=\dfrac{509}{4}$

⇒$a=\dfrac{509}{4}-\dfrac{161}{4}$

⇒$a=\dfrac{509-161}{4}=\dfrac{348}{4}$

⇒ a = 87

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