Math, asked by Preet8005, 1 year ago

In an ap of 50 terms the sum of first 10 terms is 210

Answers

Answered by afnaan94
3

In an ap of 50 terms, the sum of 1st 10 terms is 210 and the sum of its last 15 terms is 2565. find the a.p.

Answered by Anonymous
2

   \underline{  \underline{\bf{Answer}}}  :  -  \\   \implies \: 3, \: 7 \:, 11 \: ,15, \: ..........,199 \\ \\   \underline{\underline{ \bf{Step - by  - step \: explanation \: }}} :  -  \\  \\

According to the question:-

 \bf{sum \: of \: first \: 10 \: terms \:( s_{10})   = 210} \\   210 =  \frac{10}{2} \bigg (2a + (101)d \bigg) \: \\   \\ 2a + 9d = 42 \: .........(1)\\   \\ \bf{sum \: of \: last \: 15 \: terms \: ( s_{15})= 2565} \\ \\  s_{50} -s_{35} = 2565  \\  \\ 2565 =  \frac{50}{2}  \bigg(2a + (50 - 1)d \bigg)  -  \frac{35}{2} \bigg(2a + (35 - 1)d \bigg) \\  \\ 2565 = 25(2a + 49d) - 35(a + 17d)  \\  \\  2565 = 50a + 1225d - 35a - 595d \\  \\ after \: solving \: this \:  \\  \\ a + 42d = 171 \:  ...........(2) \\  \\ from \: eq(1) \: and \: (2) \\  \\eq (1) \times 42 - \: eq (2) \times 9 \\  \\ we \: get \:  \\  \\ a = 3 \: d = 4 \\

Hence required AP is →

3,7,11,15,....,199

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