Question

Help me in solving these questions so that you will get marked as brainlist thank you​

Answer 1

Topic

Arithmetic Progression

To Find

20) tₙ if a = 10 and d = 3.

21) Whether the sequence 1, 4, 7, 10,.... is an A.P. or not?

22) t₄ if tₙ = 2ⁿ - 1

Arithmetic Progression ( AP )

Any sequence with common difference between its consecutive terms is known as AP.

tₙ = a + ( n - 1 )d

where

• a = First Term of AP
• n = number of term
• d = Common Difference between terms

Solution

20) It is given that a = 10 and d = 3

And,

tₙ = a + ( n - 1 )d

So,

tₙ = 10 + ( n - 1 )( 3 )

tₙ = 10 + 3n - 3

tₙ = 3n + 7

So, tₙ = 3n + 7

21) Series :- 1, 4, 7, 10, ...........

To confirm whether the series is an AP or not, we will check the common difference and if common difference is same it means series is in AP.

Let's check common difference.

4 - 1 = 3

7 - 4 = 3

10 - 7 = 3

We can observe that common difference is same between its consecutive terms. So, this is an AP.

So, given series is in AP.

22) To find t₄, put n = 4 in given formula that is

tₙ = 2ⁿ - 1

t₄ = 2⁴ - 1

t₄ = 16 - 1

t₄ = 15

So, t₄ = 15.

Answer

So, answer of respective questions are

• tₙ = 3n + 7

• Series is in AP, and

• t₄ = 15