B) 19.8
C) 17.6
If a26-a25 = 15, then the common difference of AP is
A)3
B) 5
C)7
CA
D) 17.17
D) 15
Answers
Answer: The correct answer is 15
Explanation: This problem can be solved using the nth term of an arithmetic progression (AP) formula.
An AP's nth term is determined by:
- a_n = a_1 + (n-1)d
where d is the common difference, n is the number of terms, and a 1 is the first term.
It is stated that a 26 - a 25 equals 15. When the formula's values are substituted, we obtain:
- a_26 = a_25 + d
- a_25 = a_1 + 24d
So, (a_1 + 25d) - (a_1 + 24d) = 15
Simplifying this, we get:
- d = 15
Hence, the AP's common difference is 15.
Arithmetic Progression, or AP for short, is another name for an arithmetic sequence. It is a set of numbers where, with the exception of the first term, which itself is defined separately, each term is acquired by multiplying the previous term by a fixed amount (referred to as the common difference).
- As an example, the following would be an arithmetic progression with a first term of 2 and a common difference of 3:
- 2, 5, 8, 11, 14, 17, ..
- Each term in this series is created by adding 3 to the term before it. The first term is 2, and we keep adding 3 to produce the next terms.
Learn more about arithmetic progression here- https://brainly.in/question/11357684
Learn more about common difference of AP here- https://brainly.in/question/16703248
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EXPLANATION.
⇒ a₂₆ - a₂₅ = 15.
As we know that,
General terms of an ap.
⇒ Tₙ = a + (n - 1)d.
Using this formula in this question, we get.
⇒ [a + (26 - 1)d] - [a + (25 - 1)d] = 15.
⇒ (a + 25d) - (a + 24d) = 15.
⇒ a + 25d - a - 24d = 15.
⇒ 25d - 24d = 15.
⇒ d = 15.
Common difference : d = 15.
∴ Option [D] is correct answer.
MORE INFORMATION.
Supposition of terms in an A.P.
Three terms as : a - d, a, a + d.
Four terms as : a - 3d, a - d, a + d, a + 3d.
Five terms as : a - 2d, a - d, a, a + d, a + 2d.