Question

Consider the arithmetic sequence 6, 10, 14 ___
a.what is the common difference...
b. what is the 10th term....
c.what is it's algebraic form... ​

Answer 1

Answer:

d=4

10th term=42

x+2=y

Answer 2

$Given \: arithmetic \: sequence : 6,10,14,\ldots$

$First \: term ( a = a _{1}) = 6$

$\red{ a. Common \: difference (d)}$

$= a_{2} - a_{1}$

$= 10 - 6$

$\green { = 4 }$

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

$Here , a = 6 , d = 4 \: and \: n = 10$

$\red{ b. 10^{th} \:term \: of \: A.P }$

$= a_{10}$

$= a + 9d$

$= 6 + 9 \times 4$

$= 6 + 36$

$= 40$

$\red { 10^{th} \:term \: of \: A.P}\green { = 40 }$

$Here , a = 6 , d = 4$

$\red{c. n^{th} \:term }$

$a_{n} = a + (n-1)d$

$= 6 + ( n -1 )\times 4$

$= 6 + 4n - 4$

$= 4n + 2$

Therefore.,

$\red{ Algebraic \: form \:of \: A.P }$

$\green { a_{n} = 4n + 2 }$

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