Question

find the sum of the first 20 terms of the AP whose 2nd term is 2 and the 4 term is 8​

Answer 1

Answer:

Let a be the first term and d be the common difference of the required A.P.

Let t1 ,t2 , t3 , t4 , t5 ,............ , t20 be the required 20 terms of the A.P.

Given: t2 = 2 and t4 = 8

Solution:

We know that,

tn = a + (n-1) d...... (formula)

So, t2 = a+(2-1)d

t2=a+1d

But t2 = 2

Therefore, a+d = 2..... (1)

Also, t4 = a+3d... as per the formula

But t4=8

Therefore, a+3d=8....(2)

Subtracting (1) from (2)

We get....

2d = 6

d = 3

Substitute d=3 in eq. (1)

a+d=2

a+3=2

a=2-3

a=-1

Now the first term is -1 and and common difference of the A.P. is 3

So with the help of the first and the common difference.... we can find the first 20 terms of the A.P.

SO.. the required 20 terms are

-1,2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47,50,53,56

Hope u understand my explaination and it helps u the best....