Answer :
The arithmetic progression (AP) starts with the first term 16 and has a common difference of 5. The 15th term of the AP is 86.
Finding the Arithmetic Progression (AP) and its 15th Term
To find the AP and its 15th term, we can use the information provided about its 5th and 10th terms. We know that for an AP, any term Tn can be calculated using the formula Tn = a + (n-1)d, where a is the first term and d is the common difference.
Given that the 5th term is 36 and the 10th term is 61, we can set up two equations:
T5 = a + (5-1)d = 36
T10 = a + (10-1)d = 61
Subtracting the first equation from the second gives us:
(61 - 36) = (9d - 4d)
25 = 5d
d = 5
Now knowing d, we can substitute back into one of the equations to find a:
36 = a + 4(5)
36 = a + 20
a = 16
With the values of a and d, we can find the 15th term using the term formula:
T15 = a + (15-1)d
T15 = 16 + 14(5)
T15 = 16 + 70
T15 = 86
Therefore, the AP begins with 16 and has a common difference of 5, and its 15th term is 86.
