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1) Algebra Formulas
2) Geometry Formulas
In the Previous Blog we had seen some important concepts of Arithmetic & Geometric Progression. Click HERE to Revise that Blog.
Download following files for learning Formulas more effectively. Take the print out of these files and write your answers daily to improve your scores in 10th standard/grade.
[ Note: The following 2 files are available in the secured drive. While downloading, your email might be asked. Please provide it to download the files. I assure that your email-id will not be given to anybody. It is 100% FREE ]
2) Geometry Formulas
In the Previous Blog we had seen some important concepts of Arithmetic & Geometric Progression. Click HERE to Revise that Blog.
In this Blog, we Describe the Important Formulas of an AP & GP.
1) tn = a + (n - 1) d
2) Sn = n * (a + l)/2
3) Sn = n * [ 2 a + (n - 1) d ) ] / 2
Now we will see some examples:
Problems related to tn = a + (n - 1) d:
A) Find nth term of an AP 3, 5, 7, 9 ...
Solution:
1) Here a = 3, d = (5 - 3) = 2 so, d = 2.
2) We know that
Now we will see some examples:
Problems related to tn = a + (n - 1) d:
A) Find nth term of an AP 3, 5, 7, 9 ...
Solution:
1) Here a = 3, d = (5 - 3) = 2 so, d = 2.
2) We know that
tn = a + (n -1) d
= 3 + (n -1) (2)
= 3 + (2 n - 2)
= 1 + (2 n)
= (2 n) + 1
3) Answer: Here the nth term of an AP is tn = (2 n) + 1
B) Find first term of an AP in which d = 4 and it's 100th term is 403.
= 3 + (n -1) (2)
= 3 + (2 n - 2)
= 1 + (2 n)
= (2 n) + 1
3) Answer: Here the nth term of an AP is tn = (2 n) + 1
B) Find first term of an AP in which d = 4 and it's 100th term is 403.
Solution:
1) Here d = 4 and t100 = 403.
2) We know that
1) Here d = 4 and t100 = 403.
2) We know that
tn = a + (n -1) d
403 = a + (100 - 1)*(4)
403 = a + (99)*(4)
403 = a + (396)
a = 403 - 396
a = 7
3) Answer: Here the 1st term is a = 7
C) If nth term of an AP is m and mth term of an AP is n, then find the value of d.
403 = a + (100 - 1)*(4)
403 = a + (99)*(4)
403 = a + (396)
a = 403 - 396
a = 7
3) Answer: Here the 1st term is a = 7
C) If nth term of an AP is m and mth term of an AP is n, then find the value of d.
Solution:
1) Let " a " be the 1st term and " d " be the common difference.
2) We know that
1) Let " a " be the 1st term and " d " be the common difference.
2) We know that
tn = a + (n -1) d
3) So we,
tn = a + (n -1) d = m ----------- (1)
tm = a + (m -1) d = n ----------- (2)
Subtract equation (2) from (1) we get,
a + (n -1) d = m
a + (m -1) d = n
(-) (-) (-)
----------------------------------
(n - 1 - m + 1) * d = (m - n)
(n - m) * d = (m - n)
d = (m - n)/(n-m)
d = - 1
4) Answer: Here common difference is d = - 1
For More details Please Click HERE.
Anil Baburao Satpute
3) So we,
tn = a + (n -1) d = m ----------- (1)
tm = a + (m -1) d = n ----------- (2)
Subtract equation (2) from (1) we get,
a + (n -1) d = m
a + (m -1) d = n
(-) (-) (-)
----------------------------------
(n - 1 - m + 1) * d = (m - n)
(n - m) * d = (m - n)
d = (m - n)/(n-m)
d = - 1
4) Answer: Here common difference is d = - 1
For More details Please Click HERE.
Anil Baburao Satpute
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