Question

If the 10th term if AP is 52 and the 17th term is 20 more than the 13th term .Find the AP


​

Answer 1

Answer:- a+9d = 52

a+16d = 20 + a+12d

a-a+16d-12d = 20

4d = 20

d = 5

Putting the value of 'd' in first equation,

a+9*5 = 52

a+45 = 52

a = 7

a2 = a+d = 7+5 = 12

a3 = a+2d = 7+2*5 = 7+10 = 17

a4 = a+3d = 7+3*5 = 7+15 = 22

A.P. = 7, 12, 17, 22, .....

Hope it helps!

Plz. Mark it as the brainiest.

Answer 2

✬ AP = 7 , 12 , 17 , 22 , 27... ✬

Step-by-step explanation:

Given:

• 10th term of an AP is 52 .
• 17th term of AP is 20 more than 13th term.

To Find:

• What is the AP series.

Solution: As we know that an AP is series is given by a, a + d , a + 2d , a + 3d.....

Sum of its nth term is given by

★ a^n = a + ( n – 1 ) d ★

A/q

➙ 10th term is 52

➙ a¹⁰ = a + (10 – 1)d

➙ 52 = a + 9d....(1)

Also, 17th term is 20 more than the 13th term

➙ a¹⁷ = a¹³ + 20

➙ a + (17 – 1)d = a + (13 – 1)d + 20

➙ a + 16d = a + 12d + 20

➙ a – a + 16d – 12d = 20

➙ 4d = 20

➙ d = 20/4 = 5

Putting the value of d in equation (1)

➟ 52 = a + 9(5)

➟ 52 = a + 45

➟ 52 – 45 = a

➟ 7 = a

∴ AP series will be :- a = 7 , a + d = 7 + 5 = 12 , a + 2d = 7 + 10 = 17....so on.