Question

the 14th term of an ap is twice the 8th term if the 6th term is minus 8 find the sum of its 20th term​

Answer 1

The answer is in the attachment...

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Answer 2

☯️ CORRECT QUESTION ☯️

The 14th term of an AP is twice the 8th term if the 6th term is minus 8.Find the sum of its 20th term.

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Solution :-

Given :

▪️T14=2×T8

▪️T6 = - 8

Therefore on solving further,

=>T6=a +(n-1)d= - 8

T6=a+(6-1)d= - 8

T6=a+5d = - 8.................eq1

=>T14= a+(n-1)d

T14=a+(14-1)d

T14=a+13d....................... eq2

=>T8=a+(n-1)d

T8=a+(8-1)d

T8=a+7d...........................eq3

According to the question,

=>T14 = 2× T8

a+13d = 2×(a +7d)

a+13d=2a+14d

2a-a=13d-14d

[a= - d]

As from eq 1,

T6=a+5d = - 8

=> (-d) +5d= - 8

=> 4d= - 8

=>d= (-8/4)= (- 2)

Hence on solving eq1, we get

=>a+5(-2)= - 8

=>a - 10= - 8

=>a = 2

$The \: formula \: for \\ \: Sn =[ \frac{n}{2} (2a + (n - 1)d]$

As n = 20,

$S20 \: =[\frac{20}{2} (2 \times 2 + (20 - 1) \times ( - 1)]$

$S20 \: = 10(4 - 19) \\ S20 = 10( - 15) = ( - 150)$

So, the sum of its 20th term is (-150).

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