Question

if in an A.p S5=35,S4=22,find the 5th term

Answer 1

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Answer 2

Answer:

The fifth term is 13

Step-by-step explanation:

Let a be the first term and d be the common difference.

The formula for the nth term of an A.p is

$S=\frac{n}{2} \left [2a+(n-1)d\right ]$

Now, $S_5=35$

Thus, we have

$35=\frac{5}{2} \left [2a+4d\right ]\\\\2a+4d=14\\a+2d=7....(1)$

Now, $S_4=22$

$22=\frac{4}{2} \left [2a+3d\right ]\\\\2a+3d=11........(2)$

Multiply equation (1) by 2 and subtracting with equation (2)

4d-3d=14-11

d = 3

From equation (1), we have

a+2(3)= 7

a + 6 = 7

a = 1

Hence, the 5th term is given by

$a_5=a+(n-1)d\\a_5=1+(5-1)\cdot (3)\\a_5=1+12\\a_5=13$

The fifth term is 13