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Sequences & Series - Arithmetic - the General term.
Test Yourself 2 - Solutions.


 

Answer. T1 = 2 and d = 3.
Finding a term 1. The arithmetic sequence 7, 11 and 15:

So T1 = 7 and d = 4.

For 111 to be a member of this sequence:

111 = 7 + (n-1)×4

108 = 4n

n = 27 which is an integer.

∴ 111 is a member of the sequence.

 2. Series is 84, 78 and 72

So T1 = 84 and d = -6

∴-36 = 84 + (n - 1)(-6)

6n = 126
n = 21 - which is an integer.

So -36 is part of the series and is the 21st term.
  3. Sn = 25n - 2n2.

(i) The 2nd term = S2 - S1

S2 = 42 and S1 = 23 - so T2 = 19.

(ii) Tn = Sn - Sn-1

Sn = 25n - 2n2 and Sn-1 = 25(n-1) - 2(n-1)2

∴25n - 2n2 - (25n - 25 - 2n2 + 2n - 2) = 27 - 4n

(iii) First term less than -500.

We know that the series starts 23 + 19 - so the difference = -4

-500 = 23 + (n-1)(-4)

4n = 527

n = 131.75 - so n = 132

Substituting: T132 = 23 + 131×(-4) = -501

So -501 is the 132 term and it is the first term less than -500.
Finding a 1st term 4. 5.
Finding a difference.

6.

7.
     
Finding the number of terms

10. (i) Sum of interior angles = (n - 2)×180°

(ii) T1 = 120° and d = 5°.
  11. 12.
Given 2 terms 13.

14.

Answer.
  15.  
Miscellaneous. 17.
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  19. 20.