Question

If the 10th term of an A.P is 52 and 17th term is 20 more than the 13th term, find A.P​

Answer 1

Step-by-step explanation:

Given

10th term = a +9d = 52_i)

17th term = a + 16d

13th term = a + 12d

a+16d-(a+13d)=20 _ II)

Now use the two equations to find the value of a and d

3d =20

d=20/3

substitute value of d in any eq and then calculate a

and then form the AP

Answer 2

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: QuEsTiOn :- \: \star}}}}}$

⠀ • If the 10th term of an A.P is 52 and 17th ⠀⠀⠀⠀term is 20 more than the 13th term, find A.P.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

Given

⠀⠀⠀⠀ • a10 = 52

⠀⠀⠀⠀ • a17 = 20+a13

To Find

⠀⠀⠀⠀ • Find A.P

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

⠀

⠀⠀⠀⠀ ⠀ Using formula ❦

⠀⠀

⠀⠀⠀ ⠀ ⠀⠀ ☆ an = a+(n-1)×d ☆

⠀⠀

• a10 = 52 [ Given]

Putting values,

❥ 52= a+(10-1)×d

❥52 = a+9d________________(1)

• a17 = 20+a13 [ Given]

Putting values,

❥ a+16d= 20+a+12d

❥ 16d-12d = 20

❥ 4d= 20

❥ d= 20/4

❥ d= 5

Putting value of d in eq 1

• 52= a+9d

❥ 52= a+9×5

❥ 52= a+45

❥ a= 52-45

❥ a= 7

⠀⠀

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

The A.P is 7, 12, 17,22.