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Answer 1

Information provided with us :

• A.P. is 4.2 , 4.7 , 5.2 , 5.7
• last term (l) of that A.P. is 8.7

What we have to calculate :

• No of terms of that A.P. (n) ?

Using Formula :

We know that nth term of an A.P. is calculated by,

• $\boxed{\red{\bf{t_{n } = a+ (n - 1)d}}}$

Here,

• a is first term of the A.P.
• tn or l is the last term
• d is common difference
• n is number of terms

Performing Calculations :

We have :

• Last term or t_n is 8.7
• first term (a) is 4.2

Finding out common difference :-

Here we would be calculating the common difference (d) by subtracting the first term (a) with the second term of the A.P and so on~

$\implies \: \sf{Common \: difference (d) \: = 4.7 - 4.2}$

$\implies \: \large{\pink{\boxed{\bf{Common \: difference (d) = 0.5}}}}$

$\therefore \: \bf{\underline{Common \: difference \: (d) \: is \: 0.5 \: respectively}}$

Putting the values in the formula :-

Here we would be calculating the number of terms of that A.P. (Arithmetic progression) by substituting all the values~

$: \longmapsto \sf{8.7 = 4.2 + (n - 1) 0.5}$

$: \longmapsto$ 8.7 = 4.2 + (n - 1) × 0.5

$: \longmapsto$ 8.7 - 4.2 = (n - 1) × 0.5

$: \longmapsto \: \sf{(n - 1) \: = \: \dfrac{8.7 - 4.2}{0.5}}$

$: \longmapsto \: \sf{(n - 1) \: = \: \dfrac{4.5}{0.5}}$

$: \longmapsto \: \sf{(n - 1) \: = \: \dfrac{45 \times 10}{05 \times 10}}$

$: \longmapsto \: \sf{(n - 1) \: = \: \dfrac{450}{50}}$

$: \longmapsto \: \sf{(n - 1) \: = \: \cancel\dfrac{450}{50}}$

$: \longmapsto \: \sf{(n - 1) \: = \: \dfrac{45}{5}}$

$: \longmapsto \: \sf{(n - 1) \: = \: \cancel\dfrac{45}{5}}$

$: \longmapsto \: \sf{(n - 1) \: = \: 9}$

$: \longmapsto$ n - 1 = 9

$: \longmapsto$ n = 9 + 1

$: \longmapsto \: \red{\boxed{\bf{n \: = \:10}}}$

$\underline{\bf{Henceforth, \: 10th \: term \: of \: the \: A.P. \: is \: 8.7}}$

Additional Information :

• Arithmetic progression (A.P.) is a sequence in which each term can be found by adding a certain quantity to its preceding term
• Difference between two consecutive terms is called common difference
• Progression means it's a type of sequence in which each term is related to its predecessor and successor.

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Answer 2

Answer:

you should + 5 in each

Step-by-step explanation:

5.7, 6.2,6.7, 7.2, 7.7, 8.2

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