Question

The first term of an arithmetic sequence is 10 and the common difference is 5. Find the value of the 30th term

Answer 1

The value of the 30th term in the arithmetic sequence is 155.

Step-by-step explanation:

To find the value of the 30th term in an arithmetic sequence, we can use the formula:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

In this case, a1 = 10, d = 5, and we want to find a30.

Substituting these values into the formula:

a30 = 10 + (30-1)5

a30 = 10 + 145

a30 = 155

Therefore, the value of the 30th term in the arithmetic sequence is 155.

Answer 2

Step-by-step explanation:

First term of the sequence is 10 and common difference is 3.

a

1

​

= 10 and d = 3

Next term = a

2

​

=a

1

​

+d=10+3=13

a

3

​

=a

2

​

+d=13+3=16

Thus, first three terms of the sequence are 10, 13 and 16.

Let 100 be the nth term of the sequence.

a

n

​

=a

1

​

+(n−1)d

100=10+(n−1)3

90=(n−1)3

n−1=30

n=31, which is a whole number.

Therefore, 100 is the 31

st

term of the sequence.