Question

The sum of first six terms of an ap; s 42 .T5he ratio of its 10th term to its 30th term 1:3 .Calculate the first and the thirteenth term of an ap

Answer 1

Answer:

$\huge{\boxed{\boxed{\sf{a=2\:AND\:a13=26}}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION-}}}}}$

□S6=42

□RATIO=$\frac{a10}{a30}=\frac{1}{3}$

TO FIND:

○a1=?

○a13=?

$ratio = \frac{a10}{a30} = \frac{1}{ 3} \\ = ) \frac{a + 9d}{a + 29d} = \frac{1}{3} \\ = )3a + 27a = a + 29d \\ = )3a - a = 29d - 27d \\ = )2a = 2d \\ a = d - - - - - (1)$

□a=d

$s6 = 42 \\ = ) \frac{n}{2} (2a + (n - 1)d) = 42 \\ = ) \frac{6}{2} (2a + 5a) = 42 \\ = )7a = \frac{42}{3} \\ = )a = \frac{14}{7} \\ = )a = 2$

□a=d=2

□a13=?

$a13 = a + 12d \\ = )2 + 12 \times 2 \\ = )2 + 24 \\ = )26$

$\huge{\boxed{\boxed{\sf{a=2\:AND\:a13=26}}}}$

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