Question

For an A.P. ,if a=3, d= 5, what is the value of t11 ?​

Answer 1

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Answer 2

Answer:

Given :

• ≻ First term = 3
• ≻ Common difference = 5

$\begin{gathered}\end{gathered}$

To Find :

• ≻ $\rm{t_{11}}$

$\begin{gathered}\end{gathered}$

Using Formula :

$\longrightarrow \: \small{\underline{\boxed{\sf{a_n = a + \bigg(n - 1 \bigg) \times d}}}}$

• ➝ a = First term
• ➝ d = Common difference
• ➝ n = number of terms
• ➝ $\rm{a_{n}}$ = nth term

$\begin{gathered}\end{gathered}$

Solution :

Finding the value of $\bf{t_{11}}$ by substituting the values in the formula :

$\begin{gathered} \qquad{\longrightarrow{\sf{a_n = a + \bigg(n - 1 \bigg) \times d}}} \\ \\ \qquad{\longrightarrow{\sf{t_{11}= 3 + \bigg(11 - 1 \bigg) \times 5}}} \\ \\ \qquad{\longrightarrow{\sf{t_{11}= 3 + \bigg(10\bigg) \times 5}}} \\ \\ \qquad{\longrightarrow{\sf{t_{11}= 3 + 10 \times 5}}} \\ \\ \qquad{\longrightarrow{\sf{t_{11}= 3 + 50}}} \\ \\ \qquad{\longrightarrow{\sf{t_{11}= 53}}} \\ \\ \qquad{\bigstar{\pink{\underline{\boxed{\sf{t_{11}= 53}}}}}}\end{gathered}$

Hence the value of $\bf{t_{11}}$ is 53.

$\begin{gathered}\end{gathered}$

Learn More :

★ Formula to find the numbers of term of an AP:

$\longrightarrow{\small{\red{\underline{\boxed{\sf{n= \bigg[ \dfrac{(l - a)}{d} \bigg]}}}}}}$

★ Formula to find the tsum of first n terms of an AP:

$\longrightarrow{\small{\red{\underline{\boxed{\sf{S_n= \dfrac{n}{2} \big(a + l \big)}}}}}}$

★ Formula to find the sum of squares of first n natural numbers of an AP:

$\longrightarrow{\small{\red{\underline{\boxed{\sf{S = \dfrac{n(n + 1)(2n + 1)}{6} }}}}}}$

★ Formula to find the nth term of an AP is the square of the number of terms:

$\longrightarrow{\small{\red{\underline{\boxed{\sf{S = {(n)}^{2} }}}}}}$

★ Formula to find the sum of of an AP:

$\longrightarrow{\small{\red{\underline{\boxed{\sf{S = n(n+1)}}}}}}$

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