Answer

Verified

455.7k+ views

**Hint:**Use the general (nth) term of A.P. which is ${T_n} = a + \left( {n - 1} \right)d$. Satisfy the conditions given in the question and find the value of $a$ and $d$.

**Complete step-by-step answer:**

We know that the general (nth) term of A.P. is ${T_n} = a + \left( {n - 1} \right)d$ where $a$is the first term and $d$is the common difference.

And according to the question, the 17th term of an A.P. is 5 more than twice its 8th term. So, we have:

$ \Rightarrow {T_{17}} = 2{T_8} + 5$

Using the formula of ${T_n}$, we’ll get:

$

\Rightarrow a + \left( {17 - 1} \right)d = 2\left[ {a + \left( {8 - 1} \right)d} \right] + 5, \\

\Rightarrow a + 16d = 2a + 14d + 5, \\

\Rightarrow a - 2d = - 5 .....(i) \\

$

Further, it is given that the 11th term of the A.P. is 43. So, we have:

$

\Rightarrow a + \left( {11 - 1} \right)d = 43, \\

\Rightarrow a + 10d = 43 .....(ii) \\

$

Now, subtracting equation $(ii)$ from equation $(i)$ we’ll get:

$

\Rightarrow a - 2d - a - 10d = - 5 - 43, \\

\Rightarrow - 12d = - 48, \\

\Rightarrow d = 4 \\

$

Putting the value of d in equation $(i)$, we’ll get:

$

\Rightarrow a - 2 \times \left( 4 \right) = - 5, \\

\Rightarrow a - 8 = - 5, \\

\Rightarrow a = 3 \\

$

Putting values of $a$ and $d$in general equation, we’ll get:

$

\Rightarrow {T_n} = a + \left( {n - 1} \right)d, \\

\Rightarrow {T_n} = 3 + \left( {n - 1} \right) \times 4, \\

\Rightarrow {T_n} = 3 + 4n - 4, \\

$

$ \Rightarrow {T_n} = 4n - 1$

**Thus, the nth term of A.P. is $4n - 1$.**

**Note:**The general term of an A.P. is always a 1 degree polynomial in $n$ while the sum of first $n$ terms on the A.P. is a 2 degree polynomial in $n$.

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

10 examples of law on inertia in our daily life