Math, asked by uas88, 8 months ago

the 13 th term of Ap is 4 times its 3 rd term if the 5 th term is 16 then find the sum of its first ten terms​

Answers

Answered by ratanvoleti
1

Answer:

Step-by-step explanation:

an = a1 + (n - 1)d

Find the 13th term:

a13= a + 12d

Find the 3rd term:

a3 = a + 2d

Given that 13th term is 4 times its 3rd term:

a + 12d = 4(a + 2d)

a + 12d = 4a + 8d

3a = 4d ----------------------- [ 1 ]

Given that the 5th term is 16:

16 = a +4d

a = 16 - 4d ----------------------- [ 2 ]

Sub { 2 } into [ 1 ]:

3(16 - 4d) = 4d

48 - 12d = 4d

16d = 48

d = 3  ----------------------- sub into equation [ 2 ]

Find a:

a = 16 - 4d

a = 16 - 4(3)

a = 4

Find the nth term:

an = a1 + (n - 1)d

an = 4 + (n - 1)3

an = 4 + 3n - 3

an = 1 + 3n

Find the 10th term:

a10 = 1 + 3(10)

a10 = 31

Find the sum of the first 10 terms:

Sn = n/2 (a1 + an)

S10 = 10/2 (4 + 31)

S10 = 175

Answer: The sum of the first 10 terms is 175

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