If the common difference of an A.P. is 7, then what is a20-a11?
?
1) 64
2) 65
3) 66
4) 63
To find the value of a20 - a11 in an arithmetic progression (A.P.) with a common difference of 7, we need to determine the value of the 20th term (a20) and the 11th term (a11).
The formula to find the nth term of an arithmetic progression is given by:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
Given that the common difference (d) in this case is 7, we can substitute the values into the formula. Let's assume that the first term (a1) is a.
For the 20th term (a20):
a20 = a1 + (20 - 1) * 7
a20 = a + 19 * 7
Similarly, for the 11th term (a11):
a11 = a1 + (11 - 1) * 7
a11 = a + 10 * 7
Now, we can substitute these expressions for a11 and a20 into the equation a20 - a11 to find the required difference:
a20 - a11 = (a + 19 * 7) - (a + 10 * 7)
= a + 133 - a - 70
= 133 - 70
= 63
Therefore, the value of a20 - a11 is 63.
Hence, the correct option is 4) 63.