Question

8. In an A.P., if Sum of 5 terms is 35 & sum of 4 terms is 22, then find the 5th term.​

Answer 1

Answer:

Given : S5=35

S4=22

To Find :a5=?

Soln. S5 =35

n/2×[2a+(n-1)×d]=35

5/2×[2a+(5–1)×d]=35

5/2×[2a+4d]=35

2a+4d=35×2/5

2a+4d=14………eqn. 1

Also, S4=22

n/2[2a+(n-1)×d]=22

4/2×[2a+(4–1)×d]=22

2×(2a+3d)=22

2a+3d=11……….eqn. 2

Now, on subtracting eqn.2 from eqn.1 , we get

2a+4d-(2a+3d)=14-11

2a+4d-2a-3d=3

d=3

On putting d=5 in eqn. 1

2a+4×3=14

2a=14–12

a=1

Now, a5=a+(n-1)×d

a5=1+(5–1)×3

a5=1+12

[a5=13]

So, the 5th term in this AP is 13.