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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

1 Answer

6 votes

Final Answer:

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.

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