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SS2: MATHEMATICS - 2ND TERM

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  1. Sequence | Week 1
    2 Topics
  2. Series | Week 2
    2 Topics
    |
    1 Quiz
  3. Geometric Progression | Week 3
    2 Topics
    |
    1 Quiz
  4. Linear Equations & Formulae | Week 4
    5 Topics
    |
    1 Quiz
  5. Quadratic Equations II | Week 5
    2 Topics
  6. Quadratic Equations III | Week 6
    1 Topic
  7. Quadratic Equations IV | Week 7
    3 Topics
    |
    1 Quiz
  8. Simultaneous Equations I | Week 8
    2 Topics
  9. Simultaneous Equations II | Week 9
    2 Topics
    |
    1 Quiz
  10. Algebraic Fractions | Week 10
    5 Topics
    |
    1 Quiz



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Topic Content:

  • The Sum of Nth Term of a G.P

Finding the sum of terms in a geometric progression can be obtained with the use of formulas.

The sum of the first nth term of a G.P is given as 

Sn = \( \frac{a(r^n \: – \: 1)}{r \: – \: 1} \) (r > 1)

or

Sn = \( \frac{a(1 \: – \: r^n)}{1 \: – \: r} \)  (r < 1)

whereSnsum of GP with n terms
 athe first term
 rcommon ratio
 nnumber of terms

Sum of a G.P to Infinity:

The sum to infinity of a geometric series,

S = \( \frac{a}{1 \: – \: r} \) (-1<r<1)

 whereSsum of GP with infinitely many terms
 athe first term
 rcommon ratio
 nnumber of terms

Example 3.2.1:

If the 2nd and 5th terms of a G.P are -6 and 48 respectively, Find the sum of the first four terms. (SSCE)

Solution

T2 = ar = -6 ……….(1)

T5 = ar4 = 48 ……….(2)

divide equation (2) by equation (1)

⇒ \( \frac {ar^4}{ar} = \frac {48}{-6} \)

r3 = -8

take the cube root of both sides

\(\scriptsize \sqrt[3]{r^3} = \sqrt[3]{-8} \)

 

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