Question

after familiarizing yourself on finding the nth term of an arithmetic sequence,let us try to answer the exercises below.
find the term indicated in each of the following arithmetic sequences.
1. 2, 4, 6, ...
2. 13, 16, 19, 22 ,...
3. 99, 88, 77, 66, ...
4. 1.8, 1.4, 3.8, 1.2, ...
5. 99, 87, 75, 63, ...​

Answer 1

$Given \: A.P : 1. \: 2,4,6 , \ldots$

$First \: term (a = a_{1} ) = 2$

$Common \: difference (d) \\= a_{2} - a_{1} \\= 4 - 2 \\= 2$

$\boxed{ \pink{ n^{th} \: term (a_{n}) = a + (n-1)d }}$

$a_{n} = 2 + (n -1)2$

$\implies a_{n} = 2 + 2n - 2$

$\green { \implies a_{n} = 2n }$

$Given \: A.P : 2. \: 13,16,19,22, \ldots$

$First \: term (a = a_{1} ) = 13$

$Common \: difference (d) \\= a_{2} - a_{1} \\= 16 - 13\\= 3$

$\boxed{ \pink{ n^{th} \: term (a_{n}) = a + (n-1)d }}$

$a_{n} = 13 + (n -1)3$

$\implies a_{n} = 13 + 3n - 3$

$\green { \implies a_{n} = 3n + 10 }$

•••♪

Answer 2

Answer:

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