Final answer:
The arithmetic progression (AP) with a first term of -14, a fifth term of 2, and a last term of 62 has a common difference of 4. Using this information, it is determined that the sequence contains 20 terms.
Step-by-step explanation:
The question involves finding the number of terms in an arithmetic progression (AP) where the first term (a1) is -14, the fifth term (a5) is 2, and the last term (an) is 62. To find the number of terms, we first need to calculate the common difference (d) using the formula for the nth term of an AP: an = a1 + (n-1)d.
Using the given information for the first and fifth terms:
a5 = a1 + (5-1)d
2 = -14 + 4d
2 + 14 = 4d
16 = 4d
d = 4
The common difference is 4. Now we find the number of terms using the last term:
an = a1 + (n-1)d
62 = -14 + (n-1)4
62 + 14 = 4(n-1)
76 = 4n - 4
80 = 4n
n = 20
Therefore, there are 20 terms in the AP.