The first term of an A.P. is -2 and 11th term is 18. Find its 15th term :

Question

Accepted Answer

To find the 15th term of the arithmetic progression (A.P.) where the first term is -2 and the 11th term is 18, we can use the formula for the nth term of an A.P.:

$$ a_n = a + (n-1) \cdot d $$

where $ a $ is the first term, $ d $ is the common difference, and $ n $ is the term number.

1. **Finding the common difference ($ d $):**

We know:
   - The first term ($ a $) is -2.
   - The 11th term ($ a_{11} $) is 18.

Using the formula for the 11th term:
   $$
   a_{11} = a + (11-1) \cdot d = 18
   $$
   $$
   -2 + 10d = 18
   $$
   $$
   10d = 18 + 2
   $$
   $$
   10d = 20
   $$
   $$
   d = \frac{20}{10} = 2
   $$

2. **Finding the 15th term ($ a_{15} $):**

Now that we have the common difference $ d = 2 $, we can find the 15th term:
   $$
   a_{15} = a + (15-1) \cdot d
   $$
   $$
   a_{15} = -2 + 14 \cdot 2
   $$
   $$
   a_{15} = -2 + 28
   $$
   $$
   a_{15} = 26
   $$

Therefore, the 15th term of the A.P. is 26, which corresponds to Option 3.

**Explanation for why other options are incorrect:**

- **Option 1 (24):** This option is incorrect because, as calculated, the 15th term is 26, not 24. The calculation shows that adding 28 to the first term -2 results in 26.

- **Option 2 (25):** This option is incorrect because the arithmetic calculation clearly shows that the 15th term is 26. The difference of 2 added 14 times to the first term results in 26, not 25.

- **Option 4 (27):** This option is incorrect because the calculated 15th term is 26. The arithmetic progression with the given first term and common difference does not reach 27 at the 15th term.

Thus, the correct answer is Option 3, which is 26.