Question

Third term of an arithmetic sequence is 17 and 7th term is 25 a)find its 11th term b)write the sequence

Answer 1

Step-by-step explanation:

given

$a_{3} = 17 \: and \: a_{7} = 25$

W.K.T(we know that)

$a_{n} = a +( n - 1)d$

so

$a_{3} = a + (3 - 1)d \\ 17 = a + 2d \\ a = 17 - 2d --( i )\: \: \: \: \:$

also

$a_{7} = a + (7 - 1)d \\ 25 = a + 6d \\ 25 = 17 - 2d + 6d - (from \: i) \\ 25 - 17 = 4d \\ 8 = 4d \\ d = 2$

$take \: eq(i) \\ a = 17 - 2d \\ a = 17 - 2(2) \\ a = 17 - 4 \\ a = 13$

$a) \: a _{11} = a + (11 - 1)d \\ = 13 + 10 \times 2 \\ = 13 + 20 \\ = 33$

d)AP is 13,15,17,19,21...