Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 35, d=4?

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Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 35, d=4?

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Answer 1 · 2015-07-17T20:04:26

The explicit formula for the sequence is $a_{n} = 4 n + 31$ $color(red)( a_n = 4n+31)$ , and the first five terms are $35, 39, 43, 47, 51$ $color(red)( 35,39,43,47,51)$ .

Explanation:

We know that the common difference $d = 4$ $d = 4$ .

The general formula for an arithmetic sequence is

$a_{n} = a_{1} + (n - 1) d$ $a_n = a_1 + (n-1)d$ .

So, for your sequence, the general formula is

$a_{n} = 35 + 4 (n - 1) = 35 + 4 n - 4$ $a_n = 35 + 4(n-1) = 35 +4n-4$

$a_{n} = 4 n + 31$ $a_n = 4n+31$

$a_{1} = 35$ $a_1 = 35$

$a_{2} = 4 \times 2 + 31 = 8 + 31 = 39$ $a_2 = 4×2+31 = 8+31 = 39$

$a_{3} = 4 \times 3 + 31 = 12 + 31 = 43$ $a_3 = 4×3+31 = 12+31 = 43$

$a_{4} = 4 \times 4 + 31 = 16 + 31 = 47$ $a_4 = 4×4+31 = 16+31= 47$

$a_{5} = 4 \times 5 + 31 = 20 + 31 = 51$ $a_5= 4×5+31 = 20+31 = 51$

The first five terms are $35, 39, 43, 47, 51$ $35,39,43,47,51$ .

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Given the first term and the common difference of an arithmetic sequence how do you find the first five terms and explicit formula: a1 = 35, d=4?

1 Answer

Explanation:

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