Question

The sum of first six terms of an ap is 42 the ratio of its 10th terms to its 30th teem is 1:3.Calauclate the fiest and the thirteenth teem of tge ap

Answer 1

Answer:

First term = 2, Thirteenth term = 26

Step-by-step explanation:

Let the first term be A and common difference be D

Given that sum of first six terms = 42

∵ sum of n terms = n/2 [2a + (n-1)d],

where a = first term, d = common difference and n = number of terms

∴ 6/2[2A + (6 - 1)D] = 42

2A + 5D = 14 ----- ( i )

Also,

10th term : 30th term = 1 : 3

∴ (A + 9D) / (A + 29D) = 1/3         [∵nth term = a + (n - 1)d]

3A + 27D = A + 29 D

2A = 2D

A = D

Putting value of A = D in ( i )

2D + 5D = 14

7D = 14

D = 7

∴ Common difference = 2

∵ A = D

A = 2

∴ First term is 2

Now, thirteenth term

= A + 12D

= 2 + 12×2

=2 + 24

= 26

∴ Thirteenth term of the given AP is 26