Question

7th term of an arithmetic sequence is 30 and it's 13th term is 60.a)what is the 10th term​

Answer 1

Answer:

55

Step-by-step explanation:

d = 60-30/6

d = 5

tenth term= 30+5+5+5

=45

Answer 2

$\bf\purple{QuestioN:-}$

7th term of an arithmetic sequence is 30 and it's 13th term is 60. What is the 10th term​.

$\bf\green{AnsweR:-}$

GiveN:-

• 7th term of an AP = 30

• 13th term of the same AP = 60

To FinD:-

• The 10th term of the AP = ??

SolutioN:-

The first term of an AP = a

Then,

7th term of an AP = a + 6d

13th term of an AP = a + 12d

That is,

$\longrightarrow\bf{a+6d=30}$ --------- Eq1.

$\longrightarrow\bf{a+12d=60}$---------Eq2.

Eq2 - Eq1,

$\longrightarrow\bf{(a+12d)-(a+6d)=60-30}$

$\longrightarrow\bf{a+12d-a-6d=30}$

$\longrightarrow\bf{6d=30}$

$\longrightarrow\bf{d=\dfrac{30}{6}}$

$\longrightarrow\bf{d=5}$

On substituting value of d in Eq.1,

$\longrightarrow\bf{a+6\times5=30}$

$\longrightarrow\bf{a+30=30}$

$\longrightarrow\bf{a=30-30}$

$\longrightarrow\bf{a=0}$

The first term of the AP = 0

Actually our question is to find the 10th term of the AP,

That is,

$\longrightarrow\bf{a+9d}$

On substituting values,

$\longrightarrow\bf{0+9\times5=A_{10}}$

$\longrightarrow\bf{0+45=A_{10}}$

$\longrightarrow\bf{45=A_{10}}$

The 10th term of the AP = 45

Happy Learning!!!