Question

The ninth term of an arithmetic progression is 22 and the sum of the first 4 terms is 49.
i) Find the first term of the progression and the common difference.
The nth term of the progression is 46.
ii) Find the value of n.​

Answer 1

Answer:

a9=22

S4=49

We know that...

Sn = n/2[2a +(n-1)d]....(i)

Step-by-step explanation:

given that: a9=22;

a+(8-1)d=22

a+7d=22. ...(ii)

or a=22-7d...(iii)

now putting the value of a in (i), we get:

S4= 4/2[2(22-7d) + (4-1)d]

S4=49=2[44-14d+3d]

49=2[44-11d]

49=88-11d

or we get

11d =88+49

11d=137

from here we get value of d, and putting the value of d in (ii) ,we also get valve of a..

thanks a lot! I hope it is helpful for you ☺️❣️