Observe the given pattern 4- 0-1-01 4- 1-2-06 4- 2-3-11 4-3-4 -16 and find the 15th term-

4× 0+1=01 4× 1+2=06 4× 2+3=11 4× 3+4=16 4× 4+5=21 ∴ 1,6,11,16,21,.....15 terms are in A.P a=1, d=6 1=5 t_15=a+14d=1+14× ...

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Observe the g...

Question

Observe the given pattern
$4 \times 0 + 1 = 01$
$4 \times 1 + 2 = 06$
$4 \times 2 + 3 = 11$
$4 \times 3 + 4 = 16$ and find the $15^{t h}$ term.

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4 \times 0 + 1 = 01

4 \times 1 + 2 = 06

4 \times 2 + 3 = 11

4 \times 3 + 4 = 16

4 \times 8 + 9

1 = \frac{1}{2} \{1 \times (1 + 1)\} 1 + 2 = \frac{1}{2} \{2 \times (2 + 1)\} 1 + 2 + 3 = \frac{1}{2} \{3 \times (3 + 1)\} 1 + 2 + 3 + 4 = \frac{1}{2} \{4 \times (4 + 1)\}

(1 \times 2) + (2 \times 3) = \frac{2 \times 3 \times 4}{3}

(1 \times 2) + (2 \times 3) + (3 \times 4) = \frac{3 \times 4 \times 5}{3}

(1 \times 2) + (2 \times 3) + (3 \times 4) + (4 \times 5) = \frac{4 \times 5 \times 6}{3}

2^{6} = 64

2^{5} = 32

2^{4} = 16

2^{3} = 8

2^{2} = 4

2^{1} = ?

2^{0} = ?

2^{0}

2^{0}

3^{6} = 729

3^{5}, 3^{4}, 3^{3} . . .

3^{0}

\frac{2 \times 3 \times 5}{6}

\frac{3 \times 4 \times 7}{6}

\frac{4 \times 5 \times 9}{6}

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