The 17th term of the arithmetic progression (A.P) is given as 18.
What is defined as arithmetic progression?
An arithmetic progression (AP) is a succession in which the differences between each successive term are the same.
- An arithmetic progression is a series in which each term (except the first) is derived by adding a fixed number to the term before it.
- The following arithmetic progression formulas are frequently used to solve various AP problems for the initial term 'a' of an AP and the common difference 'd':
- Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.
- nth term of an AP: an = a + (n - 1)d
- Sum of n terms of an AP: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l defines last term of an AP.
Now, as per the given question;
- 16th term; a₁₆ = 21
- Common difference; d = -3
Then, the 17th term will be;
Apply the difference formula;
d = a₁₇ - a₁₆
a₁₇ = a₁₆ + d
a₁₇ = 21 + (-3)
a₁₇ = 21 - 3
a₁₇ = 18.
Therefore, the value of the 17th term of an AP is found to be 18.
To know more about the arithmetic progression, here
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