find the no of terms in an AP given that its first and last terms are a and 37a respectively and that its common difference is 4a
37a = a + 9*4a
so, ...
term(1) = a
term(n)
= a + (n-1)d
= a + (n-1)(4a) = 37a
(n-1)(4a) = 36a
n-1 = 9
n = 10
To find the number of terms in an arithmetic progression (AP), you need to use the formula for the nth term of an AP:
an = a + (n - 1) * d,
where 'an' is the nth term, 'a' is the first term, 'n' is the number of terms, and 'd' is the common difference.
In this case, the first term is 'a', the last term is 37a, and the common difference is 4a.
To find the number of terms, we need to first find the value of 'n' by substituting the values into the formula:
37a = a + (n - 1) * (4a).
Simplifying the equation:
37a = a + 4a(n - 1).
Combining like terms:
37a = a + 4an - 4a.
Rearranging the equation:
37a - a = 4an - 4a.
36a = 4an - 4a.
36a + 4a = 4an.
40a = 4an.
Dividing both sides by 4a:
10 = n.
Therefore, the number of terms in the arithmetic progression is 10.