in an AP the third term is equal to five times the sixth term. the second term is lesser by 3 than twice the fourth term. find the term of AP
a= -25.67 and d= 0.28
To find the terms of the arithmetic progression (AP), let's assign variables to the terms. Let's say the first term is 'a', and the common difference is 'd' (since the AP is not given explicitly).
From the given information, we can deduce two equations:
1) Third term = 5 times the sixth term:
Using the formula for the nth term of an AP, we can write:
a + 2d = 5(a + 5d)
2) Second term is lesser by 3 than twice the fourth term:
Again using the formula for the nth term, we can write:
a + d = 2(a + 3d) - 3
Now, let's solve these equations to find the value of 'a' and 'd'.
Equation 1:
a + 2d = 5a + 25d
4d = 4a
a = d
Equation 2:
a + d = 2a + 6d - 3
0 = a + 5d - 3
Now, substituting the value of 'a' from equation 1 into equation 2:
0 = d + 5d - 3
0 = 6d - 3
3 = 6d
d = 0.5
Substituting the value of 'd' back into equation 1 to find 'a':
a = d
a = 0.5
Therefore, the first term 'a' of the AP is 0.5, and the common difference 'd' is 0.5.
To find the individual terms of the AP, you can use the formula for the nth term of an AP:
Tn = a + (n - 1)d
Substituting the values we found, we can calculate the terms of the AP:
T1 = 0.5
T2 = 0.5 + (2-1)*0.5
T3 = 0.5 + (3-1)*0.5
...
and so on.
Well, just read the words and use what you know about APs:
a+2d = 5(a+5d)
a+d = 2(a+3d)-3
Now you can find a and d and answer any other questions about the sequence.
a+2d = 5(a+5d)
a+d = 2(a+3d)-3