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In an arithmetic sequence, a1 = 17 and d = 10. ?

a. Write a rule for the nth term of the sequence.
b. Use the rule to find the fourth and eleventh terms

189 day(s) ago

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jcatta21 		The general rule for writing the nth term of an arithmetic sequence is represented by the formula: an = a1 + d(n - 1), where a1 is the first term in the sequence, n = number of terms, and d = common difference between terms.

Insightfully, the common difference (d) represented in the formula provides an innuendo for finding successsive terms because the common difference (d) is represented mathematically and algebraically as d = an - a(n-1). In this case, the first term is given such as a1 = 17 with d = 10 being the common diffference. That which is meant by the above fact is that the common difference between terms of the above sequence is d = a2 - a1 = an - a(n-1) = 10.

Thus, the successive terms of the above sequence can be derived by using the common difference (d = 10) as follows:

d = a2 - a1 => (10) = a2 - (17) => a2 = 27. Given the pattern of differences between the terms with d = 10, the third, fourth, fifth, term etc can be derived. All you do is solve for the succeeding term as in a(n+1) = a(n-1) + d:

a2 = a1 + d => a2 = 27; a3 = 37; a4 = 47; a5 = 57; a6 = 67; a7 = 77; a8 = 87; a9 = 97; a10 = 107; .....an7 = n7.

Using this pattern, you can easily derive the fourth and eleventh term of the above sequence, which are:

a4 = 47
a11 = 117

an = a1 + d(n - 1) => General Rule for the nth term
a(n+1) = a(n-1) + d => Alternative Rule for an nth term

Dr. Cayo

Posted 187 dy ago

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Question Title In an arithmetic sequence, a1 = 17 and d = 10. ?
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