24Âˇ The sum of first six terms .ofan.A.P is .42. The ratio of its 1

1.	24Âˇ The sum of first six terms .ofan.A.P is .42. The ratio of its 10th term to30th.term is 1 :3. Calculate the first and 13th term of the A.P
Answer» S6 =42 a + 9d 1------------ = -------a + 29d 3 cross multiply we get 3a + 27d = a +29 d 2a - 2d = 0 ------------------ (1)its given thatsum of first six terms of an AP is 42 therefore S6 = n/2 ( 2a + (n-1) d) 42 = 6/2 ( 2a + (6-1) d) 42 = 3 (2a + 5d ) 14 = 2a +5d 2a +5d = 14 ------------------- (2) solve eq 1 and 2 2a - 2d = 02a +5d = 14 we getd= 2a = 2---------------13th term of AP= a + (n-1)d 2+ (13-1) 2 = 2+ 24 =26 Like my answer if you find it useful!

24Âˇ The sum of first six terms .ofan.A.P is .42. The ratio of its 10th term to30th.term is 1 :3. Calculate the first and 13th term of the A.P

Answer»

S6 =42

a + 9d 1------------ = -------a + 29d 3

cross multiply we get

3a + 27d = a +29 d

2a - 2d = 0 ------------------ (1)its given thatsum of first six terms of an AP is 42

therefore

S6 = n/2 ( 2a + (n-1) d)

42 = 6/2 ( 2a + (6-1) d)

42 = 3 (2a + 5d )

14 = 2a +5d

2a +5d = 14 ------------------- (2)

solve eq 1 and 2

2a - 2d = 02a +5d = 14

we getd= 2a = 2---------------13th term of AP= a + (n-1)d

2+ (13-1) 2

= 2+ 24

=26

Like my answer if you find it useful!