If the seventh term of an a.p is 29 and the 12th tern is 44 find difference and the first term
Let the first term of the arithmetic progression be 'a' and the common difference be 'd'.
The formula for the nth term of an arithmetic progression is given by:
An = a + (n-1)d
According to the problem, the seventh term is 29:
A7 = a + (7-1)d = 29
And the twelfth term is 44:
A12 = a + (12-1)d = 44
To find the difference 'd', we can subtract the equation for A7 from the equation for A12:
(A12) - (A7) = (a + 11d) - (a + 6d) = 44 - 29
5d = 15
d = 15/5
d = 3
Substituting the value of 'd' back into the equation for A7, we can find 'a':
A7 = a + (7-1)d = 29
a + 6(3) = 29
a + 18 = 29
a = 29 - 18
a = 11
Therefore, the difference is 3 and the first term is 11.