Question

the sum of 5th and 9th terms of an arithmetic progression is 40 and the sum of 8 and 14 term is 60 find sum of first 20 terms​

Answer 1

Step-by-step explanation:

your answer attached in the photo

Answer 2

Answer:

AP. Formula = a+(n - 1)(d)

5th term = a+ (5-1)d

a+4d

9th term = a+(9-1)d

a+8d

their Sum;

a+4d+a+8d = 40

2a+12d = 40 _____(i)

8th term = a+(8-1)d

a+7d

14 th term = a+(14-1)d

a+13d

their Sum ;

a+7d+a+13d = 64

2a + 20d = 64 ______(ii)

By subtracting equations (i) and (ii)

2a+20d = 64

2a+12d = 40

8d = 24

d = 24/8

⇝ d = 3

their for a = 2a+20(3)=64

2a + 60 = 64

2a = 64-60

2a = 4

a = 4/2

⇝a = 2

we got a as 2 and d as 2

so,

sum of 20 th term ;

n/2 { 2a + n -1 d }

20/2 { 2(2) + (20-1)(2)}

10 { 4 + 19(2)}

10 ( 4+ 38 )

10(42)

420

Hence, the Sum of 20th term is 420.

Step-by-step explanation: