Question

the sum of first six terms of an ap is 42 .the ratio of its 10th term is and its 30th term is 1:3. calculate the first and thirteenth term

Answer 1

First term is 2 whereas the thirteenth term is 26
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Answer 2

Answer:

a1=2

a13=26

Step-by-step explanation:

Given that sum of 6 terms is 42. That means S₆= 42. Also, n= 6.

Sₐ= n/2 [2a + (n-1)d ]

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

42= 3 [ 2a + 5d ]

2a + 5d= 14 ................. (1)

Now, Ratio of 10th and 30th term is 1:3.

We know that 10th term= a + 9d. Also, 30th term= a+ 29d

ATQ, (a+ 9d) / (a+29d) = 1/3

So, 3a + 27d = a + 29 d (cross multiplication)

2a - 2d= 0

⇒ a - d= 0 ............ (2)

Solving  (1) and (2) we get,

a= 2 and d= 2

a1=2.

a13=26

hope it will help you ; )