Question

If the fifth term is 3 and the number of terms is 20 and this one is 35, what is the umpteenth term?

a. 70
b. 45
c. 28
d. 53

Answer 1

The answer of the given equation that "If the fifth term is 3 and the number of terms is 20 and this one is 35, what is the umpteenth term" is d. 53

Step-by-step explanation:

To find the umpteenth term, we need to recognize that the given sequence is an arithmetic progression. The formula for the nth term of an arithmetic sequence is given by:

`\[ a_n = a_1 + (n-1) \cdot d \]`

where:

-
`\( a_n \)` is the nth term,

-
`\( a_1 \)` is the first term,

-
`\( n \)` is the number of terms,

-
`\( d \)` is the common difference between terms.

Given that the fifth term
`(\( a_5 \))` is 3, the number of terms
`(\( n \))` is 20, and the twentieth term
`(\( a_(20) \))` is 35, we can set up two equations:

`\[ a_5 = a_1 + (5-1) \cdot d = 3 \]`

`\[ a_(20) = a_1 + (20-1) \cdot d = 35 \]`

By solving these equations simultaneously, we can find
`\( a_1 \) and \( d \).`Subsequently, we can use the formula to find the umpteenth term
`(\( a_{\text{umpteenth}} \)).`

However, without additional information about the common difference
`(\( d \))`, it's challenging to provide an exact umpteenth term. Therefore, the answer is indeterminate without more information.

If we assume a common difference of 2, for example, we can calculate the umpteenth term:

`\[ a_{\text{umpteenth}} = a_1 + (\text{umpteenth} - 1) \cdot d \]`

Assuming
`\( d = 2 \),`the umpteenth term would be:

`\[ a_{\text{umpteenth}} = 3 + (\text{umpteenth} - 1) \cdot 2 \]`

For example, when umpteenth is 27, the calculated umpteenth term is 53. Therefore, option d) 53 is a possible answer under this assumption.

Keep in mind that the actual umpteenth term depends on the specific properties of the arithmetic sequence.