Question

af an AP,
5th term is
AP, If Se
35 and s
4=22
, then the 5 th term is​

Answer 1

Step-by-step explanation:

Ques. In an AP, if S5 = 35 and S4 = 22, what is the 5th term?

Before we start solving this question, let us know the meaning of S5 and S4.

So, here, S5 refer to the sum of the 1st, 2nd,3rd, 4th and 5th term and S4 means the sum of 1st,2nd,3rd and 4th term.

Now,let us proceed to the solution.

Sol. S5 = 1st term + 2nd term +3rd term + 4th term + 5th term = 35 ————(i)

S4 = 1st term + 2nd term + 3rd term + 4th term = 22 ————(ii)

Subtracting (ii) from (i), we get

5th term = 13.

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

hope it helps u mate

Answer 2

Answer:

$\huge{\underline{\underline{\sf{꧁AnSWer꧂}}}}$

S5=35

n=5

Formula

$sn = \frac{n}{2} (2a + (n - 1) \times d)$

$35 = \frac{5}{2} (2a + 4d)$

$\frac{35 \times 2}{5} = 2a + 4d$

$14 = 2a + 4d - - - - - (1)$

S4=22

n=4

$22 = \frac{4}{2} (2a + 3d) \\ \frac{22 \times 2}{4} = 2a + 3d \\ 11 = 2a + 3d - - - (2)$

Subtract (2) from(1)

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

Substitute value of (d) in eq (2)

$11 = 2a + 3 \times 3 \\ 11 - 9 = 2a \\ a = 1$

Now using formula

$sn = \frac{n}{2} (2a + (n - 1) \times d)$

$s5 = \frac{n}{2} (a + an) \\ 35 = \frac{5}{2} (1 + an) \\ 14 = 1 + an \\ an = 13$

nth term =13

5th term= 13