Find the 98th term of the arithmetic sequence −10,−8,−6,⋯

Question

Fatema Sutton · Accepted Answer

Step 1&amp;nbsp;The following arithmetic sequence is−10,−8,−6,⋯&amp;nbsp;Step 2&amp;nbsp;The first term&amp;nbsp;a=−10&amp;nbsp;Common difference&amp;nbsp;d=−8−(−10)=−6−(−8)=2&amp;nbsp;We know what the n-th AP term isTn=a+(n−1)⋅d&amp;nbsp;98-th term,&amp;nbsp;n=98&amp;nbsp;T98=−10+(98−1)⋅2&amp;nbsp;=−10+97⋅2&amp;nbsp;=−10+194&amp;nbsp;T98=184

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

nick1337 · Accepted Answer

Answer:184Explanation:To find the 98th term of an arithmetic sequence, we need to determine the pattern and apply the formula. In this case, the given arithmetic sequence starts with -10 and increases by 2 each time. We can represent this sequence as:an=−10+(n−1)·2 where an represents the nth term of the sequence. We can now substitute n=98 into the formula to find the 98th term.a98=−10+(98−1)·2Simplifying this expression:a98=−10+97·2Now, let&#039;s calculate the value of a98:a98=−10+194a98=184Therefore, the 98th term of the arithmetic sequence -10, -8, -6, ... is 184.

Don Sumner · Accepted Answer

The general formula for an arithmetic sequence is given by

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

, where

a_{n}

represents the

n

th term,

a_{1}

is the first term,

n

is the term number, and

d

is the common difference between consecutive terms.
In this case, the first term

a_{1}

is

- 10

and the common difference

d

is

2

since each term increases by

2

.
Using the formula, we substitute the values

a_{1} = - 10

,

n = 98

, and

d = 2

to find the 98th term:

a_{98} = - 10 + (98 - 1) \times 2

Now let's solve this equation:

a_{98} = - 10 + (98 - 1) \times 2 a_{98} = - 10 + 97 \times 2 a_{98} = - 10 + 194 a_{98} = 184

Therefore, the 98th term of the arithmetic sequence

- 10, - 8, - 6, \dots

is

184

.

Find the 98th term of the arithmetic sequence -10,-8,-6,\cdots

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