The fifth term of an arithmetic sequence is 11. If the difference between two consecutive terms is 1, what is the product of the first two terms?
a , a+d, a+2d ..... a+(n-1)d
or
an = a +(n-1)d
a5 = a + 4 (1) = 11
so
a = 7
7 * 8 = 64-8 :)
56
To find the product of the first two terms of an arithmetic sequence, we need to determine the value of the first term.
Let's assume the first term of the arithmetic sequence is 'a', and the common difference between consecutive terms is 'd'.
Given that the difference between two consecutive terms is 1, we can write the second term as 'a + d', the third term as 'a + 2d', and so on.
Since we are told that the fifth term of the sequence is 11, we can write this as:
a + 4d = 11
Now, let's substitute the value of 'a + 4d' into the equation:
a + 4d = 11
a = 11 - 4d
To find the product of the first two terms, we multiply 'a' and 'a + d':
(a) * (a + d)
Substitute the value of 'a' from the previous equation:
(11 - 4d) * (11 - 4d + d)
Simplify the expression:
(11 - 4d) * (11 - 3d)
Expand the expression:
121 - 33d + 12d - 4d^2
Combine like terms:
121 - 21d - 4d^2
The product of the first two terms is 121 - 21d - 4d^2.