## Arithmetic Sequence Worksheet Solution3

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In the page arithmetic sequence worksheet solution3
you are going to see solution of each questions from the arithmetic sequence
worksheet.

(9) Find n so that the nth terms of the
following two A.P’s are the same

1 , 7 ,13 ,19, ………………. and
100 , 95 , 90 ,………..

**Solution:**

tn = a + (n - 1) d

nth term of the first
sequence

a = 1 d = t₂-t₁

= 7-1

d = 6

tn = 1 + (n-1) 6

tn = 1 + 6 n – 6

tn = 6 n – 5
-----(1)

nth term of the second
sequence

a = 100 d = t₂-t₁

= 95 - 100

d = -5

tn = 100 + (n-1) (-5)

tn = 100 - 5 n + 5

tn = 105 - 5 n -----(2)

(1) = (2)

6 n – 5 = 105 – 5 n

6 n + 5 n = 105 + 5

11 n = 110

n =110/11

n = 11

Therefore 11th terms of the given sequence are
equal.

(10) How many two digit numbers are divisible by 13?

**Solution:**

10, 11, 12,………… 99

Now we need to find how many
terms from this sequence are divisible by 13

The first two digit number
divisible by 13 is 13; the next two digits number divisible by 13 is 26 and 39
so on. The last two digit numbers which are divisible by 13 is 91.

13 , 26, 39, …………….. 91

Now we need to find how many
terms are there in this sequence for that let us use formula for n.

n = [(L-a)/d] + 1

a = 13 d = 26 – 13 L = 91

d = 13

n = [(91 - 13)/13] + 1

n = (78/13) + 1

n = 6 + 1

n = 7

7 two digit numbers are
divisible by 13.

(11) A TV manufacturer has
produced 1000 TVs in the seventh year and 1450 TVs in the tenth year. Assuming
that the production increases uniformly by a fixed number every year, find the
number of TVs produced in the first year, find the number of TVs produced in
the first year and 15th year.

**Solution:**

Number of TVs produced in
the seventh year = 1000

Number of TVs produced in the tenth year =
1450

t7 = 1000

t10 = 1450

a + 6 d = 1000 ----- (1)

a + 9 d = 1450 ----- (2)

(1) – (2)

Subtracting second equation from first
equation

** **a + 6 d = 1000

** **a + 9 d = 1450

(-) (-)
(-)

------------------

-3d
= -450

d = -450/(-3)

d = 150

Substitute d = 150 in the
first equation

** ** a
+ 6(150) = 1000

a + 900 = 1000

a = 1000 -900

a = 100

Therefore number of TVs produced
on the first year is 100

To find number of TVs
produced in the 15th year year we have to find the 15th
term of the A.P

tn = a + (n-1) d

t15 = 100 + (15-1) 150

t15 = 100 + 14(150)

= 100 + 2100

= 2200

arithmetic sequence worksheet solution3 arithmetic sequence worksheet solution3