an AP has 15 terms and a common difference of 3.find the first and last term if it 120.
why do you waste our time posting the same problem over?
When someone sees it and can help, they will. Till then, getting impatient won't do you any good.
Good
To find the first and last term of an arithmetic progression (AP) given the number of terms and the common difference, we can use the following formulas:
1) Formula to find the n-th term of an AP:
an = a1 + (n - 1)d
2) Formula to find the sum of an AP:
Sn = (n/2)(a1 + an)
Given information:
Number of terms (n) = 15
Common difference (d) = 3
Sum (Sn) = 120
We need to find the first term (a1) and the last term (an).
To find the first term (a1), we can use the formula for the n-th term:
a1 = an - (n - 1)d
Now we substitute the known values:
120 = a1 + (15 - 1) * 3
Simplifying:
120 = a1 + 14 * 3
120 = a1 + 42
Subtracting 42 from both sides:
a1 = 78
So, the first term (a1) of the arithmetic progression is 78.
To find the last term (an), we can use the formula for the n-th term again:
an = a1 + (n - 1)d
Substituting the known values:
an = 78 + (15 - 1) * 3
Simplifying:
an = 78 + 14 * 3
an = 78 + 42
an = 120
Therefore, the last term (an) of the arithmetic progression is 120.