Question

Find the sum of first 25 terms of an



a.P. Whose nth term is 1-4n.

Answer 1

Nth term = 1 - 4n

Let n be 1, so

a1 = 1 - 4 (1)

a1 = 1- 4

a1 = -3

Let n be 2

a2 = 1 - 4(2)

a2 = 1-8

a2 = -7

Let n be 3

a3 = 1 - 4(3)

a3 = 1- 12

a3 = -11

Let n be 25

a25 = 1 - 4 (25)

a25 = 1- 100

a25 = -99

So we get our AP sequence

-3 , -7 , -11 ....... -99

Now we will find a , d ,and l from the above AP sequence

a = -3

d = -4

l = -99

So formula for sum of n terms of AP when last term is given is

$sn = \frac{n}{2} (a + l)$

Now putting the above values

S25 = 25/2 [-3 + (-99)]

S25 = 25/2(-3-99)

S25 = 25× 51

S25 = 1275

So sum of first 25 terms of given AP is 1275.

Hope it helps