Question

if the sum of first 14th terms of an A.P is 1050 and its first term us 110 find the 20th rerm?______________________ please explain properly in long way please​

Answer 1

Answer:

first term is 110

sum of 14 term is 1050

14[2a+(14-1)d]/2=1050

7(220+13d)=1050

220+13d=150

13d=150-220

13d= -70

d= -70/13

20th term =a+19d

=110+19(-70/13)

=110-1330/13

=110-102.30

=7.70

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Answer 2

Given :

$\sf a = 110 \\ \\\sf n = 14 \\ \\\sf s_n = 1050$

To Find :

• 20th term of the A.P

Solution :

$\sf\frac{n}{2} \bigg [2a + (n - 1)d \bigg] = s_n \\ \\ \sf\frac{14}{2} \bigg [2 \times 110 + (14 - 1)d \bigg] = 1050 \\ \\\sf 7 \big(220 + 13d \big) = 1050 \\ \\\sf 220 + 13d = \frac{1050}{7} \\ \\\sf 220 + 13d = 150 \\ \\\sf13 d = 150 - 220 \\ \\\sf d = \frac{-70}{13}$

To find 20th term

$\sf a_{20} = a + 19d \\ \\\sf a_{20} = 110 + 19 \times \frac{-70 }{13} \\ \\\sf a_{20} =110 - \frac{133}{13} \\ \\\sf a_{20} = \frac{1430 - 1330}{13} \\ \\\sf a_{20} = \frac{140}{13} \\ \\ \large\boxed{ \sf \green {a_{20} =10.7 }}$

20th term of AP is 11 approx.