Question

If third term and fifth term of an A.P. are 13 and 25 respectively, find

its 7th term.

(A) 30 (B) 33 (C) 37 (D) 3​

Answer 1

Answer:

37

Step-by-step explanation:

if there is difference of 12 in 3rd and 5th term then difference between 5th and 7th term is 12...

as it is in ap

so answer will be 37

I hope it help u, plz mark this answer as brainliest answer

Answer 2

Solution

Given :-

• If third term and fifth term of an A.P. are 13 and 25

Find :-

• 7th terms of A.P.

Explanation

Let,

• First terms = a
• Common Defference = d

Using Formula

$\boxed{\underline{\tt{\red{\:T_{n}\:=\:a+(n-1)d}}}}$

Where

• n = Number of terms

Case 1.

• If, n = 3

==> T3 = a + (3 - 1)d

==> 13 = a + 2d___________(1)

Case 2.

• If, n = 5

==> T5 = a + (5 - 1)d

==> 25 = a + 4d_________(2)

Subtract equ(1) & equ(2)

==> -2d = -12

==> d = 12/2

==> d = 6.

keep in equ(2)

==> a + 4 × 6 = 25

==> a = 25 - 24

==> a = 1

So,Now calculate 7th terms

Where

• a = 1
• d = 6

==> T7 = a + 6d

keep Value of a & d

==> T7 = 1 + 6 × 6

==> T7 = 1 + 36

==> T7 = 37

Hence

• 7th terms will be = 37

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