Question

In an arithmetic sequence with the third term 17 and the eleventh term 73, find the 100th term.

Answer 1

To find the 100th term of an arithmetic sequence, use the formula for the nth term and solve a system of equations using the provided terms.

Step-by-step explanation:

To find the 100th term of an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

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 between consecutive terms.

In this case, we are given that the third term (a3) is 17 and the eleventh term (a11) is 73. We can use these values to form two equations:

17 = a1 + 2d (equation 1)

73 = a1 + 10d (equation 2)

Solving these equations simultaneously will give us the values of a1 and d. Once we have those values, we can substitute them into the formula to find the 100th term.

Answer 2

Third term = a+2d
Eleventh term = a+ 10d
73-17 = a+10d -a - 2d
56 = 8d
d =7
Sub -> a+2d = 17
a+2(7) = 17
a=3
100th term = a+99d
= 3+99(7)
= 696