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BY
Dr. I. UMA MAHESWARI
Principal
Peniel Rural College of Education,Vemparali,
Dindigul District
iuma_maheswari@yahoo.co.in
Ex 2.7
Solution:
(i) a = 6, r = 3
tn = arn-1
t1 = ar1-1 = ar0 = a = 6
t2 = ar2-1 = ar1 = 6 × 3 = 18
t3 = ar3-1 = ar2 = 6 × 32 = 54
∴The 3 terms are 6, 18, 54, ….
The 3 terms are 1000, 400, 160, ……………
Solution:
G.P = 729, 243, 81 ……
t7 = ?
Solution:
(i) 4, 8, 16, …… 8192
Solution:
In a G.P
tn = arn-1
t9 = 32805
t6 = 1215
t12 = ?
Let
t9 = ar8 = 32805 ………(1)
t6 = ar5 = 1215 ………. (2)
Answer:
Here r = 2, t8 = 768
t8 = 768 (tn = arn-1)
a. r8-1 = 768
ar7 = 768 …..(1)
10th term of a G.P. = a.r 10-1
= ar9
= (ar7) × (r2)
= 768 × 22 (from 1)
= 768 × 4 = 3072
∴ 10th term of a G.P. = 3072
Solution:
If a, b, c are in A.P
t2 – t1 = t3 – t2
b – a = c – b
2b = c + a
To prove that 3a, 3b, 3c are in G.P
⇒ 32b = 3c+a + a [Raising the power both
sides]
⇒ 3b.3b = 3c.3a
⇒ Common ratio is same for 3a,3b,3c
⇒ 3a, 3b, 3c forms a G.P
∴ Hence it is proved .
Solution:
Offer A
Starting salary ₹ 20,000
Annual increase 6%
At the end of
III year ,salary = 22472 + 1348 =
23820
∴ IV year salary = ₹ 23820
Offer B
Starting salary = ₹ 22,000
Salary as per OptionA = ₹ 23820
Salary as per Option B = ₹ 24040
∴ Option B is better.
Solution:
a, b, c are three consecutive terms of an AP.
∴ Let a, b, c be a, a + d, a + 2d respectively ………… (1)
x, y, z are three consecutive terms of a GP.
∴ Assume x, y, z as x, x.r, x.r2 respectively ……… (2)
PT : xb-c , yc-a , za-b = 1
Substituting (1) and (2) in LHS, we get
LHS = xa+d-a-2d × (xr)a+2d-a × (xr2)a-a-d
= (x)-d . (xr)2d (xr2)-d
2g. Pedagogy of mathematics   part II (numbers and sequence - ex 2.7)

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2g. Pedagogy of mathematics part II (numbers and sequence - ex 2.7)

  • 1. BY Dr. I. UMA MAHESWARI Principal Peniel Rural College of Education,Vemparali, Dindigul District iuma_maheswari@yahoo.co.in
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  • 24. Solution: (i) a = 6, r = 3 tn = arn-1 t1 = ar1-1 = ar0 = a = 6 t2 = ar2-1 = ar1 = 6 × 3 = 18 t3 = ar3-1 = ar2 = 6 × 32 = 54 ∴The 3 terms are 6, 18, 54, ….
  • 25. The 3 terms are 1000, 400, 160, ……………
  • 26. Solution: G.P = 729, 243, 81 …… t7 = ?
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  • 28. Solution: (i) 4, 8, 16, …… 8192
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  • 30. Solution: In a G.P tn = arn-1 t9 = 32805 t6 = 1215 t12 = ? Let t9 = ar8 = 32805 ………(1) t6 = ar5 = 1215 ………. (2)
  • 31. Answer: Here r = 2, t8 = 768 t8 = 768 (tn = arn-1) a. r8-1 = 768 ar7 = 768 …..(1) 10th term of a G.P. = a.r 10-1 = ar9 = (ar7) × (r2) = 768 × 22 (from 1) = 768 × 4 = 3072 ∴ 10th term of a G.P. = 3072
  • 32. Solution: If a, b, c are in A.P t2 – t1 = t3 – t2 b – a = c – b 2b = c + a To prove that 3a, 3b, 3c are in G.P ⇒ 32b = 3c+a + a [Raising the power both sides] ⇒ 3b.3b = 3c.3a ⇒ Common ratio is same for 3a,3b,3c ⇒ 3a, 3b, 3c forms a G.P ∴ Hence it is proved .
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  • 37. Solution: Offer A Starting salary ₹ 20,000 Annual increase 6%
  • 38. At the end of III year ,salary = 22472 + 1348 = 23820 ∴ IV year salary = ₹ 23820
  • 39. Offer B Starting salary = ₹ 22,000 Salary as per OptionA = ₹ 23820 Salary as per Option B = ₹ 24040 ∴ Option B is better.
  • 40. Solution: a, b, c are three consecutive terms of an AP. ∴ Let a, b, c be a, a + d, a + 2d respectively ………… (1) x, y, z are three consecutive terms of a GP. ∴ Assume x, y, z as x, x.r, x.r2 respectively ……… (2) PT : xb-c , yc-a , za-b = 1 Substituting (1) and (2) in LHS, we get LHS = xa+d-a-2d × (xr)a+2d-a × (xr2)a-a-d = (x)-d . (xr)2d (xr2)-d