Find an increasing A P in which the sum of the first 3 terms is 27 and the sum of - Maths - Sequences and Series

Question

Find an increasing A P in which the sum of the first 3 terms is
27 and the sum of their squares is 275?

Ajanta Trivedi · Accepted Answer

let the first three terms of the AP be (a-d) , a , (a+d).

sum of first three terms = 27

$a - d + a + a + d = 27 3 a = 27 a = \frac{27}{3} = 9$

sum of their squares is 275.

$(a - d)^{2} + a^{2} + (a + d)^{2} = 275 (9 - d)^{2} + 9^{2} + (9 + d)^{2} = 275 81 + d^{2} - 18 d + 81 + 81 + d^{2} + 18 d = 275 2 d^{2} + 243 = 275 2 d^{2} = 275 - 243 = 32$

$d^{2} = \frac{32}{2} = 16 d = \pm \sqrt{16} d = \pm 4$

since the AP is an increasing AP. thus the common difference is positive and d = 4.

therefore first term of the AP = 9-4 = 5

and the common difference =4

the AP is 5 , 9 , 13, 17 , 21, ...........

hope this helps you.

cheers!!

Find an increasing A.P in which the sum of the first 3 terms is 27 and the sum of their squares is 275?