Q: What is the nth term for 2 6 12 20 30 42?

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The difference between the terms increases by 2 each time. 20-12=8 30-20=10 42-30=12 56-42=14 ... f(n)=(n+2)(n+3)

here t1=2 t2=6 t3=12 t4=20 t5=30 the nth term is n(n+1) for t1 = 1(1+1)=2 for t2=2(2+1)=6 for t3=3(3+1)=12 for t4=4(4+1)=20 for t5=5(5+1)=30 for tn=n(n+1)

> since the value rises by nine at each step and the first term is 12 the formula for > the nth term is: 12+(n-1)*9 Which simplifies to Sn = 9n + 3

Clearly here the nth term isn't n25.

90

Say if you had the pattern 15 20 25 30 35 40 45 50 To find the nth term you have to see what the gap between the numbers is. In our case this is 5. Then you have to find out what the difference between the gap and the first number. In this sequence it is 10. So your answer would be..... 5n+10 That's how you find the nth term.

This is an arithmetic progression. In general, If an A.P. has a first term 'a', and a common difference 'd' then the nth term is a + (n - 1)d. In the sequence shown in the question, the first term is 0 and the common difference is 5, therefore the nth term is, 0 + (n - 1)5. This can be rearranged to read : 5(n - 1) For example : the 7th term is 30 : 5(7 - 1) = 5 x 6 = 30.

96

Looks like 57: 12+9=21, +9=30, +9=39, +9=48, +9=57.

6n+10

The nth term is 7n-5 and so the 6th term will be 37

When n=30, 3n-1 = 89 .

n'th term: n^2 + 5

3 x 10(n-1)

Just plug in 30 for n in 3n-1. The answer is 89.

The sequence is 2 larger than the 7 times table. The nth term can be expressed as 7n + 2.

four hundred and nity six

Wow you really can't spell.

1. -52. 103. -154. 205. -256. 307. -358. 409. -45

35

Well, since the nth term is 2n+6, therefore First term = 2(1)+6 =8 Second term is 2(2) +6 = 10 Third term is 2(3) +6 = 12 Hence, their some = S3=3(2(a)+(3-1)d)/2 ====>3(2(8)+2(2))/2 ====>3(20)/2=30 Which means that this is an arithmetic sequence where a=8 and d=2 What you need to do is replace (n) with the number of the term you want to find, and there is your answer.

The LCM of 12, 20, and 30 is 60

t(n) = 5 - 7n for n = 1, 2, 3, ... The difference between each term is -7, therefore the nth term will be: t(n) = -2 + -7 × (n - 1) = -2 + 7n + 7 = 5 - 7n

t(n) = 3n2 + n = n(3n + 1)

10

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