Question

In an arithmetic progression, 25th term is 70 more than the 15th term, then the common difference is

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

The Correct Option is C

In an arithmetic progression (A.P.), the general term is given by: 

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

Given that the 25th term is 70 more than the 15th term:

\( a_{25} = a_{15} + 70 \)

Using the general formula:

\( a + (25-1)d = a + (15-1)d + 70 \)

\( a + 24d = a + 14d + 70 \)

Canceling \( a \) from both sides:

\( 24d - 14d = 70 \)

\( 10d = 70 \)

\( d = 7 \)

Thus, the common difference is: \( 7 \).

Answer 2

In an arithmetic progression (AP), the formula for the nth term is given by:
a_n = a + (n-1)d
where a is the first term and d is the common difference. Given that the 25th term is 70 more than the 15th term, we can express these terms as follows:
a₂₅ = a + 24d
a₁₅ = a + 14d
According to the problem, a₂₅ = a₁₅ + 70. Substituting the expressions, we get:
a + 24d = a + 14d + 70
Cancel a from both sides:
24d = 14d + 70
Subtract 14d from both sides:
10d = 70
Divide both sides by 10:
d = 7
Therefore, the common difference is 7.