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→Which day is Pi Day ?
1. When we combine Algebra and Geometry - this feature is not as good in CaRMetal.
1. When we combine Algebra and Geometry - this feature is not as good in CaRMetal.
2. When we combine statistics (spreadsheets) , with algebra, charts - Geometry - this feature is not there in CaRMetal.
2. When we combine statistics (spreadsheets) , with algebra, charts - Geometry - this feature is not there in CaRMetal.
=P th term of an AP is Q and Q th term of an AP is P . Then find PQ th term ?=
'''Mallikarjun Sudi, Ghs Yelhari''' All maths teachers pls solve this problem
P th term of an AP is Q and Q th term of an AP is P . Then find PQ th term ?
''' Sneha Titus, University Resource Centre, Azim Premji University'''
This is a very nice problem. Here is the solution that I worked out.
Let the nth term be Tn = a + (n‒1)d, where a is the first term and d is the common difference.
Given: Tp = q = a + (p‒1)d
And Tq = p = a + (q‒1)d
So Tp ‒Tq = q ‒ p = a + (p‒1)d ‒[a + (q‒1)d]
q ‒ p = pd ‒ d ‒ qd + d
q ‒ p = (p ‒ q) d
∴ d = = ‒ 1
And since Tq = p = a + (q‒1)d,
p = a + (q ‒1)(‒1) = a ‒q + 1
so that a = p + q ‒1
Now, Tpq = a + (pq‒1)d = a + (pq – 1)(‒1) = a ‒pq + 1 = p + q ‒1 ‒pq + 1 = p + q ‒pq
Example T2 = 4 and T4 = 2, what is T8
T2 = 4 = a + (2‒1)d = a + d
T4 = 2 = a + (4‒1)d = a + 3d
T2 ‒T4 = 4 ‒ 2 = a + d ‒[a + 3d] = – 2d
2 = ‒2d
∴ d = ‒1
And T2 = 4 = a + (2‒1)(‒1) = a ‒1
∴ a = 4 + 1 = 5
And T8 = a + (8‒1)d] = a +7 d = a ‒ 7 = 5 ‒ 7 = ‒2
The A.P with a = 5, d = ‒1 is
5, 4, 3, 2, 1, 0, ‒1, ‒2,……….
Notice that T2 = 4 and T4 = 2 and T8 = ‒2
= Which day is Pi Day ? =
= Which day is Pi Day ? =