Question

10th term of an ap is 30 and 7th term is 8 find 17th term?​

Answer 1

Answer:

look

Step-by-step explanation:

10th = 30

which means

30=a+(10-1)d

30=a+9d

30-9d=a    -------------------------------1

now, it is given that

7th=8

8=a+(7-1)d

8=a+6d

now by using 1

8=30-9d+6d

8=30-3d

8-30=-3d

-22=-3d

d=22/3

now by putting this value in 1

30=a+9(22/3)

30=a+66

a=30-66

a= -36

now for 17th term

= -36+(17- 1) 22/3

= - 36 + 16* 22/3

= - 36 + 352/3

= (-108 + 352)/3

=224/3

Answer 2

Answer:

let a & d be the first term and the common difference respectively

$t_{10} = 30\\\\t_{10} = a + (n - 1)d\\\\30 = a + (10 - 1)d\\\\30 = a + 9d\\\\a = 30 - 9d$

$t_{7} = 8\\\\t_{7} = a + (n - 1)d\\\\8 = a + (7 - 1)d\\\\8 = 30 - 9d + 6d\\\\8 - 30 = -3d\\\\28 = 3d\\\\d = \frac{28}{3}$

now putting the value of d

$a = 30 - 9(\frac{28}{3} )\\a = 30 - 84\\a = - 54$

$t_{17} = a + (n - 1)d\\\\t_{17} = - 54 + (17 - 1)\frac{28}{3} \\\\t_{17} = - 54 + \frac{16 * 28}{3} \\\\t_{17} = - 54 + \frac{448}{3}\\\\t_{17} = \frac{-62 + 448}{3}\\\\t_{17} = \frac{386}{3}$

I hope it helps....