study the pattern and give the next number in each sequence. Then write the rule in finding the nth term on the space provided 1.) 3, 6, 9, 12,___-rule:_____ 2.) 1, 4, 9, 16,___-rule:_____ 3.) 1/2, 1/3, 1/4, 1/5,___-rule:____ 4.) 1, 2, 4, 7, 11, 16, 22,___-rule:____ 5.) 3, 1, -1, -3,___-rule:____. Created by Maluisab45. Math

5,___-rule:____ 4.) 1, 2, 4, 7, 11, 16, 22,___-rule:____ 5.) 3, 1, -1, -3,__

kuleggs

1. 15

Rule: 3n

2. 25

Rule: n^2

3. 1/6

Rule: 1/(n+1)

4. 29

Rule: 2^(n-1)

5. -5

Rule: -2n+5

Maluisab45 thankyou po imamark ko po kayu na brainliest pag may nag answer pa po nito

jackdaniel012998 sa 4. a_8=2^(8-1) = 128 not 29 right?

kuleggs yeah my bad. i admit that that is wrong. your no. 3 is wrong as well

kuleggs and your 1 and 5 cant be used as rules because it is too general

jackdaniel012998 Bruh. So igonna tell my prof theyre wrong

kuleggs your answer is 1/(1+(n-1)) right? it can be simplified to 1/n. if you substitute 1 to n, the answer is 1. the answer should be 1/2 based on first term of the given sequence

jackdaniel012998

Answer:

1. 15 - RULE : $a_n=a_1+(n-1)d$

2. 25 - RULE : $a_n=n^{2}$

3. $\frac{1}{6}$ - RULE : $a_n=\frac{1}{1+(n-1)}$

4. 29 - RULE : $a_n=\frac{n(n-1)}{2} +1$

5. -5 - RULE : $a_n=a_1+(n-1)d$

Step-by-step explanation:

If you want me to explain just comment. So I can edit. Thanks.

$a_n$ = the nᵗʰ term in the sequence

$a_1$ = the first term in the sequence

$d$ = the common difference between terms

$r$ = the common ratio between terms

3, 6, 9, 12, __ (Apply the rule)

$d=6-3=3\\a_5=a_1+(n-1)d\\a_5=3+(5-1)3\\a_5=3+(4)3\\a_5=15$

1, 4, 9, 16,__ (Apply the rule)

$a_n=n^{2}\\a_5=5^{2}\\a_5=25$

1, 1/2, 1/3, 1/4, 1/5, __ (Apply the rule)

$a_n=\frac{1}{1+(n-1)}\\a_6=\frac{1}{1+(6-1)}\\a_6=\frac{1}{1+(5)}\\a_n=\frac{1}{6}$

1, 2, 4, 7, 11, 16, 22,__ (Apply the rule)

$a_n=\frac{n(n-1)}{2} +1\\a_8=\frac{8(8-1)}{2} +1\\a_8=\frac{8(7)}{2} +1\\a_8=\frac{56}{2} +1\\a_8=28 +1\\a_8=29$

3, 1, -1, -3,__ (Apply the rule)

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16 votes Thanks 31

jackdaniel012998 n^2 is also a formula. Mahahanap mo padin 10th term nya gamit the same rule you say or formula rather.

kuleggs yeah but the rule in no. 1 should be a_n = 3n

jackdaniel012998 Okay let say rule mo sa 4 is a_n=2^(n-1) pano mo nakuha yung 29 if that is your rule?

cmyzamora Thanks❤❤

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