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Find the 7th term in the following sequence: $1, 4, 7, 10, \dots$ $1, 4, 7, 10, cdots$ ?

1 Answer

Sep 26, 2016

$19$ $color(green)(19)$

Explanation:

The sequence appears to be an arithmetic sequence with a difference between terms of $3$ $color(blue)(3)$ .

In general given a first term: $a_{1}$ $color(red)(a_1)$
and a difference between successive terms: $a_{n} - a_{n - 1} = d$ $a_n-a_(n-1)=color(blue)(d)$

the $n$ $n$ th term can be calculated as $a_{n} = a_{0} + d \cdot (n - 1)$ $a_n=color(red)(a_0)+color(blue)(d) * (n-1)$

Therefore the $7$ $7$ th term of the given sequence should be
$XXX a_{7} = 1 + 3 \cdot (7 - 1) = 19$ $color(white)("XXX")a_7=color(red)(1)+color(blue)(3) * (7-1) = 19$

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