Question

In an AP, the 3rd term is 4 times its 1st term and 6 th term is 17. The first term is: (a) 2 (b) 5 (c) 8 (d) 11h​

Answer 1

The first term of the A.P is 2

Step-by-step explanation:

given:

a3=4a

a+2d=4a

2d=3a

d=3a/2--------i

also,a6=17

a+5d=17

a+5*3a/2=17------------(from i)

a+15a/2=17

17a/2=17

17a=34

a=2

Answer 2

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Given that in an AP , the third term is four time the first time

Let the first term be a and common difference be d

= a + 2d = 4× a

= 2d = 3a

Given that the sixth term is 17

= a +5d = 17

$= \frac{2d}{3} + 5d \: = 17$

$= d = \frac{3}{17} \times 17 = 3$

therefore we get d = 3 and a = 2d/ 3 = 2

so the given series is correct