Find the 5^("th ") term of the arithmetic sequence -4x-8,2x-13,8x-18,dots Answer:

Find Common Difference: To find the 5th term of an arithmetic sequence, we first need to determine the common difference (d) between consecutive terms. The common difference can be found by subtracting the first term from the second term. Calculation: (2x - 13) - (-4x - 8) = 2x - 13 + 4x + 8 = 6x - 5Calculate 5th Term: Now that we have the common difference, we can find the 5th term by adding the common difference to the previous term four times (since we already have the first term). The nth term of an arithmetic sequence is given by the formula: a_n = a_1 + (n - 1)d For the 5th term (n=5), the formula becomes: a_5 = a_1 + (5 - 1)d Calculation: a_5 = (-4x - 8) + (5 - 1)(6x - 5)Simplify Expression: Simplify the expression for the 5th term by distributing and combining like terms. Calculation: a_5 = (-4x - 8) + 4(6x - 5) = (-4x - 8) + (24x - 20) = 20x - 28

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Q. Find the

5^{\text {th }}

term of the arithmetic sequence

-4 x-8,2 x-13,8 x-18, \ldots

\newline

Answer:

Find Common Difference: To find the $5^{\text{th}}$ term of an arithmetic sequence, we first need to determine the common difference ( $d$ ) between consecutive terms. $\newline$ The common difference can be found by subtracting the first term from the second term. $\newline$ Calculation: $(2x - 13) - (-4x - 8) = 2x - 13 + 4x + 8 = 6x - 5$
Calculate $5$ th Term: Now that we have the common difference, we can find the $5$ th term by adding the common difference to the previous term four times (since we already have the first term). $\newline$ The nth term of an arithmetic sequence is given by the formula: $a_n = a_1 + (n - 1)d$ $\newline$ For the $5$ th term $(n=5)$ , the formula becomes: $a_5 = a_1 + (5 - 1)d$ $\newline$ Calculation: $a_5 = (-4x - 8) + (5 - 1)(6x - 5)$
Simplify Expression: Simplify the expression for the $5^{\text{th}}$ term by distributing and combining like terms. $\newline$ Calculation: a_5 = (\(-4x - $8$ ) + $4$ ( $6$ x - $5$ ) = ( $-4$ x - $8$ ) + ( $24$ x - $20$ ) = $20$ x - $28$