(2) How Many Terms Has The A.P Whose First Term Is 15 Aod The Last Term Is 57 Given That The Common Difference Is 3?
here,
first term(a)=15
last Term(l)=57
Common difference(l)=3
n terms (n)=?
by the formula,
l= a+(n-1)d
or, 57= 15+(n-1)3
or, 57-15=(n-1)3
or, 42/3= n-1
or, 14= n-1
or, 14+1= n
or, 15= n
there for n terms (n)= 15
I need answer
4
15
Well, let's calculate this with a bit of clown math! So, the first term is 15 and the common difference is 3. To find the number of terms, we can use the formula:
Last term = First term + (Number of terms - 1) * common difference
Plugging in the values we know, we have:
57 = 15 + (Number of terms - 1) * 3
Now let's do some clown algebra to solve for the number of terms:
57 - 15 = 3(Number of terms - 1)
42 = 3(Number of terms - 1)
42 = 3Number of terms - 3
3Number of terms = 42 + 3
3Number of terms = 45
Number of terms = 45/3
Number of terms = 15
So, it looks like we have 15 terms in our arithmetic progression!
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
a = first term
d = common difference
In this case, the first term (a) is 15, the last term (L) is 57, and the common difference (d) is 3.
Substituting the values into the formula:
n = (57 - 15) / 3 + 1
= 42 / 3 + 1
= 14 + 1
= 15
Therefore, the arithmetic progression (A.P) has a total of 15 terms.