Question

An A.P. consists of 43 terms , if the sum of five middle most terms is 195 , then the sum of the A.P. is ​

Answer 1

Answer:

1677

Step-by-step explanation:

The 5 middle most terms are

29th, 21st, 22nd, 23rd, 24th

According to question,

$a + 19d + a + 20d + a + 21d + a + 22d + a + 23d = 195$

$5a + 105d = 195$

$a + 21d = 39 \: \: \: \: \: \: \: \: .....(i)$

To find : Sum of 43 terms

$= \frac{43}{2} (2a + 42d)$

$= \frac{43}{2} \times 2(a + 21d)$

$= 43 \times 39 \: \: \: \: \: \: \: \: (from \: eq.(i))$

= 1677