Question

if 7th and 13th term of an AP be 34 and 64 than 18th term of an AP is​

Answer 1

Answer:

a7=a+6d

a13=a+12d

a+6d=34. (take it equation 1st)

a+12d=64. (take it equation 2nd)

By i and ii

a +6d=34. (do it by elimination method)

a+12d=64

a will be cancelled and

-6d=-30

d=5

put the value of d in equation 1st

a+6(5)=34

a=34-30

a=4

a18=a+17d

a18=4+17(5)

a18=4+85

a18=89

Answer 2

GIVEN:

• 7th term = 34
• 13th term = 64

TO FIND:

• What is the 18th term of an AP ?

SOLUTION:

We have

• $\sf{ a_7 = 34}$

➸ a + 6d = 34

➸ a = 34 –6d...❶

• $\sf{{a}_{13} = 64}$

➸ a + 12d = 64...❷

Put the value of 'a' from equation 1) in equation 2)

➸ 34 –6d + 12d = 64

➸ 6d = 64 –34

➸ 6d = 30

➸ d = $\sf{\cancel\dfrac{30}{6}}$

❮ d = 5 ❯

Now, put the value of 'd' in equation 1)

➸ a = 34 –6 $\times$ 5

➸ a = 34 –30

❮ a = 4 ❯

To find the 18th term of an AP, we use the formula:-

$\large{\boxed{\bf{\star \: a_n = a + (n-1) \times d \: \star}}}$

According to question:-

➸ $\sf{{a}_{18}}$ = 4 + (18 –1) $\times$ 5

➸ $\sf{{a}_{18}}$ = 4 + 17 $\times$ 5

➸ $\sf{{a}_{18}}$ = 4 + 85

❮ $\bf{{a}_{18}}$ = 89❯

❝ Hence, the 18th term of an AP is 89 ❞

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