Question

If 7th term of an Arithmetic progression is 13 and 10th term is 19. Find the 23rd term​

Answer 1

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• 7th term is 13

• 10th term is 19

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• 23rd Term

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

$\\ \boxed{ \sf \: a_{n} = a + (n - 1)d }$

Here ,

• a(n) = nth term

• n = number of terms

• d = common difference

• a = 1st term

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So,

We know , 7th term is 13

13 = a + (7-1)d

13 = a + 6d ㅤㅤㅤㅤ(i)

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Also , 10th term is 19.

19 = a + (10-1)d

19 = a + 9dㅤㅤㅤㅤ(ii)

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Subtracting eqⁿ (ii) by eqⁿ(i) ....

13-19 = a+6d-(a+9d)

-6 = a+6d-a-9d

-6 = -3d

d = 2

→ Putting d = 2 in eqⁿ (i)

13 = a + 6(2)

13 = a + 12

a = 1

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Now ,

23rd term = a + (23-1)d

23rd term = 1 + 22(2)

23rd term = 1+44

Hence , 23rd term is 45.