Given that the $50 ^ { \text {th } }$ term of an arithmetic sequence is $259$and the common difference is $5$, find the first three terms
A) $15,20,25$
B) $13,18,23$
C) $13,18,24$
D) $14,19,24$
E) $10,15,20$

Question

Quizplus · Accepted Answer

To find the first term of an arithmetic sequence, we need to work backwards from the given term with the formula:

$$a_n = a_1 + (n-1)d$$

where:
$a_n$ = the given term
$a_1$ = the first term (to be found)
$d$ = common difference
$n$ = the term number

Substituting the given values, we have:

$$259 = a_1 + (11-1)(5)$$

Simplifying, we get:

$$259 = a_1 + 50$$

$$a_1 = 259 - 50 = 209$$

So the first term is 209.

To find the second term, we add the common difference of 5:

$$a_2 = a_1 + d = 209 + 5 = 214$$

Similarly, to find the third term, we add 5 again:

$$a_3 = a_2 + d = 214 + 5 = 219$$

Therefore, the first three terms are 209, 214, and 219, which corresponds to choice D.

Given That The 50th 50 ^ { \text {th } }50th Term of an Arithmetic Sequence Is

Given That The $50 ^ { \text {th } }$ Term of an Arithmetic Sequence Is