An ap has 15 term and a common different-3 find its first and last term if it's sum is 15
Answer
To find the first and last terms of an arithmetic progression (AP) when given the number of terms, common difference, and the sum, we can use the formulas:
First term (a) = Sum of terms (S) - [(n - 1) x common difference (d)]
Last term (l) = First term (a) + (n - 1) x common difference (d)
Given:
Number of terms (n) = 15
Common difference (d) = -3
Sum of terms (S) = 15
Using the formula, we can substitute the values and find the first and last terms of the AP.
First term (a) = 15 - [(15 - 1) x (-3)]
= 15 - [14 x (-3)]
= 15 + 42
= 57
Last term (l) = 57 + (15 - 1) x (-3)
= 57 + 14 x (-3)
= 57 + (-42)
= 15
Therefore, the first term of the AP is 57 and the last term is 15.
15/2 (2a+14(-3)) = 15
solve for a and then get a+14d