Master Mind

**Given**:S_{n} = 4n^{2} - 7n

**Step by step** explanation:

**(i) Sum of 23 terms **

S_{n} = 4n^{2} - 7n ............. (**i**)

Replace n by 23 we have,

S_{23} = 4(23)^{2} - 7(23)

= 4 × 529 - 161

= 2116 - 161

= 1955 **Answer**

**(ii) 15**^{th} term

a_{15} = S_{15} - S_{14}

S_{15} = 4(15)^{2} - 7(15) = 4 × 225 - 105 = 900 - 105 = 795

S_{14} = 4(14)^{2} - 7(14) = 4 × 196 - 98 = 784 - 98 = 686

Now, a_{15} = S_{15} - S_{14}

= 795 - 686

= 109 **Answer**

(iii) n^{th} term

a_{n} = S_{n} - S_{n-1}

Given, S_{n} = 4n^{2} - 7n

Replace n by n-1 we have

S_{n-1} = 4(n-1)^{2} - 7(n-1)

= 4(n^{2} - 2n + 1) - 7n + 7

= 4n^{2} - 8n + 4 - 7n + 7

= 4n^{2} - 15n + 11 ............. (ii)

Now Applying equation (i) and (ii) in formula a_{n} = S_{n} - S_{n-1}

a_{n} = (4n^{2} - 7n) - (4n^{2} - 15n + 11)

= 4n^{2} - 7n - 4n^{2} + 15n - 11

= 8n - 11

Therefore, a_{n} = 8n - 11 **Answer**

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*-Answered by ***Master Mind** On 11 July 2019:09:42:19 PM