Question

Solve this question

The sum of first 3 term is 27 and sum of their square is 293. Then find sum of first 15 terms

(see the you will get after answering)​

Answer 1

Answer:

660 is the sum of first 15 terms

Step-by-step explanation:

let the three terms be

(a - d), a, (a + d)

sum of the three terms = 27

a - d + a + a + d = 27

3a = 27

a = 27/3 = 9

sum of their squares = 293

${(a - d)}^{2} + {a}^{2} + {(a + d)}^{2} = 293 \\ {a}^{2} - 2ad + {d}^{2} + {a}^{2} + {a}^{2} + 2ad + {d}^{2} = 293 \\ 3 {a}^{2} + 2 {d}^{2} = 293 \\ 3( {9}^{2}) + 2 {d}^{2} = 293 \\ 3(81) + 2 {d}^{2} = 293 \\ 243 + 2 {d}^{2} = 293 \\ 2 {d}^{2} = 293 - 243 \\ 2 {d}^{2} = 50 \\ {d}^{2} = \frac{50}{2} = 25 \\ d = \sqrt{25} = 5$

a = 9 d = 5

sum of first 15 terms

Sn = n/2 (2a + (n-1)d)

$= \frac{15}{2} (2(9) + 14(5)) \\ = \frac{15}{2} (18 + 70) \\ = \frac{15}{2} \times 88 \\ = 15 \times 44 \\ = 660$

hope you get your answer