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Natalie Goodwin

Feb 20, 2025

Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74. -20.5 -151 -22.75 -144

Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74. -20.5 -151 -22.75 -144
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8 Answers

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Jonathon Rolfson

Feb 20, 2025

Arithmetic sequence:an=a1+(n-1)dd=-112/16=-7 D)-144... Show More
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Jonathon Rolfson

Feb 20, 2025

- 53Step-by-step explanation:For a sequence to be arithmetic sequence then there must be a common difference (d). Common difference is given by :d = - = - ...From the sequence given :a = -1d = -3 - (-1 ) d = -3 + 1d = -2The formula for nth term of an arithmetic sequence is given as : = a + ( n - 1 ) dwhere n is the number of terms , therefore, the 27th term will be = a + (27 - 1 ) dsubstituting the value of a and d , we have = - 1 + (26) x -2 = -1 -52 = -53Therefore , the 27th term = - 53... Show More
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Jonathon Rolfson

Feb 20, 2025

Step-by-step explanation:use arithmetic sequence to find the rule for nth term where 'a1' is the first term and d is the differencefirst term is 38 , solve for dSubtract 38 from both sides, divide both sides by 16Now we find 26 term using a1= 38 and d=-7... Show More
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Jonathon Rolfson

Feb 20, 2025

Hello : the general terme is : an = ap +(n-p)r   n, p in N and r in R let n=17 and p =1a17 = a1+(17-1)r-74 = 38 +16r16r =-112r = -7an = a1 +(n-1)ra27 =38+26(-7) =−144... Show More
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J
Jonathon Rolfson

Feb 20, 2025

In order to solve for a nth term in an arithmetic sequence, we use the formula written as:an = a1 + (n-1)dwhere an is the nth term, a1 is the first value in the sequence, n is the term position and d is the common difference.First, we need to calculate for d from the given values above.  a1 = 38 and a17 = -74an = a1 + (n-1)d-74 = 38 + (17-1)dd = -7The 27th term is calculated as follows:a27 = a1 + (n-1)da27= 38 + (27-1)(-7)a27 = -144 > OPTION D... Show More
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