FIND THE NUMBER OF TERMS IN THE A.P 11,14,17...83
a = 11
d = 3
term(n) = a + (n-1)d
83 = 11 + (n-1)(3)
72 = 3n - 3
3n = 75
n = 25
83 is the 25th term
check:
term(25) = a + 24d
= 11 + 24(3) = 83
Dont understand, help me
To find the number of terms in an arithmetic progression (A.P.), you can use the following formula:
Number of terms = (Last term - First term) / Common difference + 1
In this case, the first term is 11, the last term is 83, and the common difference is 14 - 11 = 3. Let's substitute these values into the formula:
Number of terms = (83 - 11) / 3 + 1
Number of terms = 72 / 3 + 1
Number of terms = 24 + 1
Number of terms = 25
Therefore, the number of terms in the given arithmetic progression is 25.
To find the number of terms in an arithmetic progression (A.P.), you can use the formula:
n = (l - a) / d + 1
Where:
n = number of terms
l = last term of the A.P.
a = first term of the A.P.
d = common difference between terms
In this case, the first term (a) is 11, the last term (l) is 83, and the common difference (d) is 3, as the A.P. increases by 3 in each term.
Now we can substitute these values into the formula to find the number of terms:
n = (83 - 11) / 3 + 1
n = 72 / 3 + 1
n = 24 + 1
n = 25
Therefore, there are 25 terms in the given arithmetic progression (A.P.) 11, 14, 17, ..., 83.