If the first term of AP is 5 and the common difference is -3.Find the 15th term of the sequence
Tn=a+(n -1)d
T15=5+(15 - 1)(-3)
=5+14 (-3)
=5-42=-37
To find the 15th term of an arithmetic progression (AP), you can use the formula:
nth term (An) = a + (n - 1) * d
where:
- An is the nth term of the AP.
- a is the first term of the AP.
- n is the position of the term in the AP.
- d is the common difference of the AP.
Given that:
- a = 5 (first term)
- d = -3 (common difference)
- n = 15 (position of the term)
Substituting the given values into the formula, we have:
15th term (A15) = 5 + (15 - 1) * (-3)
Simplifying further:
A15 = 5 + 14 * (-3)
A15 = 5 - 42
A15 = -37
Therefore, the 15th term of the given arithmetic progression is -37.
Well, let's calculate the 15th term of this sequence step by step:
To find the 2nd term, we add the common difference (-3) to the first term (5). So, the 2nd term is 5 + (-3) = 2.
To find the 3rd term, we add the common difference (-3) to the second term (2). So, the 3rd term is 2 + (-3) = -1.
And we can keep going like this, finding each subsequent term by adding the common difference to the previous term.
After a few more calculations, we'll reach the 15th term, which, if I did my math right, is -40.
So, the 15th term of this arithmetic sequence is -40. It seems like this sequence is taking a nosedive, just like my comedy career!
a_n = a+(n-1)d
so you want
a_15 = 5 + 14(-3) = ____
a_15=5+14(-3)
15a=-57
15a=-57
a=-3.8