Question

The sum of first 8 term of an ap is hundred and the sum of first 19 term is 551 find ap

Answer 1

Answer:

2, 5, 8, 11 ..........

Step-by-step explanation:

sum of 8 terms = 100

sum of 19 terms = 551

$s8 = \frac{8}{2} (2a + 7d) = 100 \\ 2a + 7d = \frac{100 \times 2}{8} \\ 2a + 7d = 25 \: \: \: \: \: \: \: equ \: (1) \\ \\ s19 = \frac{19}{2} (2a + 18d) = 551 \\ 2a + 18d = \frac{551 \times 2}{19} \\ 2a + 18d = 58 \: \: \: \: \: \: equ \: (2) \\ subtract \: equ\: (2) - (1) \\ we \: get \: \\ 11d = 33 \\ d = \frac{33}{11} = 3 \\ substitute \: d \: value \: in \: equ \: (1) \\ 2a + 7d = 25 \\ 2a + 7(3) = 25 \\ 2a + 21 = 25 \\ 2a = 25 - 21 = 4 \\ a = \frac{4}{2} = 2 \\ \\ the \: ap \: is \: \\ a \: \: \: a + d \: \: \: a + 2d \: \: \: a + 3d \\ 2 \: \: \: 5 \: \: \: 8 \: \: \: 11$