Question

the sum of first three terms in an Ap is 24 and the sum of their squares is 224 .find the first three terms of AP. ( solve stp by stp and in a paper) YOU WILL BE A BRAN LIST IF YOU ANSWER

Answer 1

Let the first three terms be ( a - d ), a ( a+ d ).

3a - d + d = 24

a = 24 / 3 = 8

Sum of their square = 224

( a - d ) ^2 + a^2 + ( a + d ) ^2 = 224

a^2 + d^2 - 2ad +a^2 +a^2 + d^2 - 2ad = 224

3a^2 + 2d^2 = 224

3 ( 8 ) ^2 + 2d^2 = 224

64 × 3 + 2d^2 = 224

192 + 2d^2 = 224

2d^2 = 224 - 192

2 d^2 = 32

d^2 = 32 / 2 = 16

d = 4

First term = a = 8

Second term = a +d = 8 +4 = 12

Third term = a + 2d = 8 + 8 = 16

Answer 2

first term is 8

second term is 12

third term is 16