find the number of terms in an ap given that its first and last number are 13 and -23 respectively if the common difference is -9
Since -23 = 13+4d, there are 5 terms.
So S5 = 5/2 (13-23) = 90
To find the number of terms in an arithmetic progression (AP), you can use the formula:
Number of terms = (Last term - First term) / Common difference + 1
Given:
First term (a₁) = 13
Last term (aₙ) = -23
Common difference (d) = -9
Using the formula, we can calculate the number of terms:
Number of terms = (-23 - 13) / -9 + 1
Number of terms = (-36) / -9 + 1
Number of terms = 4 + 1
Number of terms = 5
So, the number of terms in the arithmetic progression is 5.
To find the number of terms in an arithmetic progression (AP), we can use the formula:
\(n = \dfrac{{a - l}}{{d}} + 1\)
where:
- \(n\) represents the number of terms in the AP,
- \(a\) represents the first term of the AP,
- \(l\) represents the last term of the AP, and
- \(d\) represents the common difference between the terms of the AP.
In this case:
- \(a = 13\) (the first term),
- \(l = -23\) (the last term), and
- \(d = -9\) (the common difference).
Now, substitute these values into the formula and calculate the number of terms:
\(n = \dfrac{{a - l}}{{d}} + 1\)
\(n = \dfrac{{13 - (-23)}}{{-9}} + 1\)
\(n = \dfrac{{13 + 23}}{{-9}} + 1\)
\(n = \dfrac{{36}}{{-9}} + 1\)
\(n = -4 + 1\)
\(n = -3\)
The number of terms in this arithmetic progression is -3. However, the number of terms cannot be negative. Hence, it is not possible to have -3 terms in an arithmetic progression. Please check the given information and calculation.