List the first 10 terms of each of these sequences.

a) the sequence that begins with 2 and in which each successive term is 3 more that the preceding term

b) the sequence that lists each positive integer three limes, in increasing order

c) the sequence that lists the odd positive integers in increasing order, listing each odd integer twice

d) the sequence whose nth term is

e) the sequence that begins with 3, where each succeeding term is twice the preceding term

f) the sequence whose first term is 2. second term is 4, and each succeeding term is the sum of the two preceding terms

g) the sequence whose nth term is the number of bits in the binary expansion of the number n (defined in Section 4.2)

h) the sequence where the nth term is the number of letters in the English word for the index n

Step-1:

In this problem we need to find the first 10 terms of the sequences.

a) The sequence begins with 2 and each successive term is 3 more that the preceding term.

Let us consider ,

Therefore , the first 10 terms of the sequence is : 5 , 8, 11, 14 , 17 , 20 , 23 , 26 and 29.

Step-2:

b)

We know that the positive integers starts with one.

Let us consider , .

, since sequence that lists each positive integer three times , in increasing order.

Then the next integer is two.

So, , since sequence that lists each positive integer three times , in increasing order.

Then the next integer is three.

So, , since sequence that lists each positive integer three times , in increasing order.

Tenth term is .

Therefore , the first 10 terms of the sequence is : 1, 1, 1, 2, 2, 2, 3, 3, 3, and 4.

Step-3:

c) We know that the odd positive integers starts with one.

Let us consider , .

, since sequence that lists the odd positive integers in increasing order , listing each odd integer twice.

Then the next odd integer is three.

So, , since sequence that lists the odd positive integers in increasing order , listing each odd integer twice.

Then the next odd integer is five.

So, , since sequence that lists the odd positive integers in increasing order , listing each odd integer twice.

Then the next odd integer is seven.

So, , since sequence that lists the odd positive integers in increasing order , listing each odd integer twice.

Then the next odd integer is nine

Therefore , the first 10 terms of the sequence is : 1 , 1, 3,3,5,5,7,7,9 and 9.

Step-4:

d) Note : n! = (1)(2)(3)..........(n)

.

Consider , term .

If n = 1 , then

If n = 2 , then .

If n = 3 , then .

If n = 4 , then .

If n = 5 , then .

If n = 6 , then

If n = 7 , then

If n = 8 , then

If n = 9 , then

If n = 10 , then .

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