Question

if a5 - a3 = 14 and seventh term of the AP is 22, then the first term of the AP is
(A) 22
(B) 20
(C) -22
(D) -20

Answer 1

Answer:

(D) -20

Step-by-step explanation:

a5 can be written as a+4d and a3 can be written as a+2d. Now, according to question,

a5 - a3 = 14

Or, a+4d - (a+2d) = 14

Or, a+4d - a-2d = 14

Or, 4d - 2d = 14

Or, 2d = 14

Or, d = 7

Now, it is also given that the seventh term is 22. So, a7 = 22. It can be written as a+6d = 22.

Put the value of d in this.

So, a + 6(7) = 22

Or, a + 42 = 22

Or, a = 22 - 42

Or, a = -20

So, first term of the AP is a = -20.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

if $\sf{a_5 - a_3 = 14}$ and seventh term of the AP is 22, then the first term of the AP is

(A) 2

(B) 20

(C) -22

(D) - 20

EVALUATION

Let for the given AP

First term = a

Common Difference = d

Then

$\sf{ a_3= a + (3 - 1)d = a + 2d }$

$\sf{ a_5 = a + (5 - 1)d = a + 4d }$

Now it is given that

$\sf{a_5 - a_3 = 14}$

$\sf{ \implies \: (a + 4d) - (a + 2d)= 14}$

$\sf{ \implies \:2d= 14}$

$\sf{ \implies \:d= 7}$

Again seventh term

$= \sf{a + (7 - 1)d}$

$\sf{ = a + 6d}$

$\sf{ \implies \:a + 6d= 22}$

$\sf{ \implies \:a + (6 \times 7)= 22}$

$\sf{ \implies \:a + 42= 22}$

$\sf{ \implies \:a = - 20}$

Hence first term = - 20

FINAL ANSWER

Hence the correct option is (D) -20

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