. How many terms are there in an AP whose first and fifth terms are - 14 and 2 respectively and the last term is 62.

To find the number of terms in an Arithmetic Progression (AP), we first need to find the common difference (d).

Step 1: Find the common difference The common difference (d) can be found using the formula: d = (a5 - a1) / (5 - 1), where a5 is the fifth term and a1 is the first term.

Substituting the given values, we get: d = (2 - (-14)) / (5 - 1) = 16 / 4 = 4.

Step 2: Find the number of terms The formula to find the nth term (an) of an AP is: an = a1 + (n - 1) * d, where a1 is the first term, n is the number of terms, and d is the common difference.

We know that the last term (an) is 62, a1 is -14, and d is 4. Substituting these values into the formula, we get: 62 = -14 + (n - 1) * 4.

Solving this equation for n, we get: n = (62 + 14) / 4 + 1 = 76 / 4 + 1 = 19 + 1 = 20.

So, there are 20 terms in the given AP.