Question

the nth term of an ap is given by minus 4 and + 15 find the sum of first 20 terms of this AP​

Answer 1

Given:

The nth term of an ap is given by minus 4 and + 15

To find:

Find the sum of first 20 terms of this AP​

Solution:

From the given information, we have the data as follows.

The nth term of an ap is given by minus 4 and + 15

⇒ T_n = -4n + 15

Using this, we will first the first two terms of the series.

So, we have,

T_1 = -4 (1) + 15 = 11

T_2 = -4 (2) + 15 = 7

The common difference is calculated as follows.

d = T_2 - T_1

= 7 - 11

d = - 4

Now, we will find the sum of first 20 terms of this AP​.

S_n = n/2 [2a + (n - 1) d]

S_n = 20/2 [2 × 11 + (20 - 1) (-4)]

S_n = 10 [22 - 76]

S_n = 10 × -54

S_n = -540

Therefore, the sum of  first 20 terms of this AP​ is -540.