Question

6,13 .20 form an ap then find the 100th term

Answer 1

Given :-

• first term = a = 6
• common difference = 20 - 13 = 13 - 6 = 7

To Find :-

• 100th term of AP .

Solution :-

we know that,

• an = a + (n - 1)d .
• a = first term .
• d = common difference .
• n = nth term .

so,

→ a100 = 6 + (100 - 1)7

→ a100 = 6 + 99 * 7

→ a100 = 6 + 693

→ a100 = 699 (Ans.)

Hence, 100th term of AP is 699.

Answer 2

Step-by-step explanation:

$\underline{\underline{\maltese\: \: \textbf{\textsf{Given}}}}$

• First term, a = 6.
• Common difference = 20 - 13 = 13 - 6 = 7.

$\underline{\underline{\maltese\: \: \textbf{\textsf{To\ Find}}}}$

• We have to find out the 100th term of A.P.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Solution}}}}$

• The 100th term of A.P is 699.

$\underline{\underline{\maltese\: \: \textbf{\textsf{Formula\ Used}}}}$

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

~ Where,

• $\sf {a_n\ is\ the\ n^{th}\ term\ in\ the\ sequence.}$
• $\sf {a\ is\ the\ first\ term.}$
• $\sf {d\ is\ the\ common\ difference.}$
• $\sf {n\ is\ the\ n^{th}\ term.}$

$\underline{\underline{\maltese\: \: \textbf{\textsf{Calculations}}}}$

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

• On substituting the values :-

$\sf \mapsto {a_{100}\ =\ 6\ +\ (100\ -\ 1)7}$

$\sf \mapsto {a_{100}\ =\ 6\ +\ 99 \times 7}$

$\sf \mapsto {a_{100}\ =\ 6\ +\ 693}$

$\sf \mapsto {\red {a_{100}\ =\ 699.}}$

${\therefore{\underline{\sf{Hence\ the\ 100^{th}\ term\ of\ A.P\ is\ \bf 699.}}}}$