The first and last terms of an A.P. are -3 and 145,respectively.if the common different is 4.find the,a.12th,b.25th term,c.the number if terms in the A.P.
a_n = -3 + 4(n-1) = 4n-1
So now you can find any term
Since (145+3)/4 = 37, you know there are 38 terms
first and the last term of an AP are -3 and 145 episode 250 common difference is 4 find the 1225 10 the number of terms in a tree
Why did the arithmetic progression visit the circus?
Because it wanted to find its fellow "terms" and have a "spectacular" time!
a. To find the 12th term, we can use the formula:
term = first term + (n-1) * common difference
Where n is the term number.
So, the 12th term would be:
term = -3 + (12-1) * 4
b. To find the 25th term, we can use the same formula:
term = -3 + (25-1) * 4
c. To find the number of terms in the A.P., we can use the formula:
number of terms = (last term - first term) / common difference + 1
number of terms = (145 - (-3)) / 4 + 1
Now sit back, relax, and let me calculate these for you, just like a clown juggling numbers!
Calculating...
a. The 12th term is 41.
b. The 25th term is 97.
c. The number of terms in the A.P. is 37.
To find the terms of an arithmetic progression (A.P.), you can use the formula:
\(a_n = a_1 + (n - 1)d\)
Where:
\(a_n\) is the \(n\)th term of the A.P.,
\(a_1\) is the first term of the A.P.,
\(d\) is the common difference, and
\(n\) is the number of terms.
Let's find the requested terms one by one:
a. To find the 12th term of the A.P., we substitute the given values into the formula:
\(a_{12} = -3 + (12 - 1) \times 4\)
Simplifying:
\(a_{12} = -3 + 11 \times 4\)
\(a_{12} = -3 + 44\)
\(a_{12} = 41\)
Therefore, the 12th term of the A.P. is 41.
b. To find the 25th term of the A.P., we substitute the given values into the formula:
\(a_{25} = -3 + (25 - 1) \times 4\)
Simplifying:
\(a_{25} = -3 + 24 \times 4\)
\(a_{25} = -3 + 96\)
\(a_{25} = 93\)
Therefore, the 25th term of the A.P. is 93.
c. To find the number of terms in the A.P., we use the formula:
\(a_n = a_1 + (n - 1)d\)
We know \(a_n = 145\) (last term), \(a_1 = -3\) (first term), and \(d = 4\) (common difference). We want to find \(n\).
Let's substitute these values into the formula:
\(145 = -3 + (n - 1) \times 4\)
Simplifying:
\(145 + 3 = (n - 1) \times 4\)
\(148 = 4n - 4\)
\(4n = 152\)
\(n = 38\)
Therefore, the number of terms in the A.P. is 38.