Answer:
answer
Explanation:
To find the number of terms in an arithmetic progression (AP) with the last term of 81 we need to determine the common difference (d) first.
Using the formula for the nth term of an AP:
a_n = a_1 + (n-1)d
We can plug in the values given in the problem:
a_1 = 3 (first term)
a_5 = 9 (fifth term)
Using the formula for the fifth term:
a_5 = a_1 + (5-1)d
9 = 3 + 4d
4d = 6
d = 6/4 = 1.5
Now we have the common difference d = 1.5.
Using the formula for the nth term again this time with the last term:
a_n = a_1 + (n-1)d
Plugging in the values:
81 = 3 + (n-1)(1.5)
81 - 3 = (n-1)(1.5)
78 = 1.5n - 1.5
Adding 1.5 to both sides:
79.5 = 1.5n
Dividing by 1.5:
n = 79.5 / 1.5
n = 53
Therefore the number of terms in the AP is 53 if the last term is 81.