Question

In an AP. the first term is 100 and common difference is 50, then find the

third term.​

Answer 1

Step-by-step explanation:

ANSWER:-

Given:-

• First term as 100
• Common difference as 50

To find:-

The third term

Let's Do!

$\sf{a_n = a + (n-1)d }$

Where:-

• an is the nth term
• a is the first term
• n is the number of terms
• d is the common difference.

$\sf{a_n = a + (n-1)d }$

$\sf{a_3 = 100 + 2 \times 50 }$

$\sf{a_3 = 100 + 100 }$

$\sf{a_3 = 200 }$

So, the required answer is 200.

Remember that it is only in the case of AP or Arithemtic Progression this formula is applied.

Answer 2

Step-by-step explanation:

$\large {\sf{\pmb{\underline{\underline{Given\ that:-}}}}}$

★ First term = 100.

★ Common difference = 50.

$\large {\sf{\pmb{\underline{\underline{To\ find:-}}}}}$

★ In this question we have to find the third term of A.P.

$\large {\sf{\pmb{\underline{\underline{Using\ Concept:-}}}}}$

★ Formula of calculating A.P.

$\large {\sf{\pmb{\underline{\underline{Using\ Formula:-}}}}}$

$\sf {\bigstar\ a_n\ =\ a\ +\ (n\ -\ 1)d}$

Where :-

• an = nth term.
• a = first term.
• n = number of terms.
• d = common difference.

$\large {\sf{\pmb{\underline{\underline{Solution:-}}}}}$

➽ The third term of the A.P is 200.

$\large {\sf{\pmb{\underline{\underline{Full\ solution:-}}}}}$

~ By applying the values, we get :-

$\sf \mapsto {a_n\ =\ a\ +\ (n\ -\ 1)d}$

$\sf \mapsto {a_3\ =\ 100\ +\ 2 \times 50}$

$\sf \mapsto {a_3\ =\ 100\ +\ 100}$

$\bf \mapsto {a_3\ =\ {\red {200.}}}$

∴ Hence, 3rd term of A.P = 200.