Question

please answer this question ​

Answer 1

Given :

• AP :- 6,10,14,18......174

To find :

• Number of terms

Formula used :

• Common difference = b - a

• Tn = a+(n-1)d

where:-

• a = first term
• b = second term
• n = number of terms
• d = common difference
• Tn = nth term

Solution :

In the given AP , a = 6 and b = 10

Therefore , Common difference = b - a

⟹ Common difference = 10 - 6

⟹ Common difference = 4

Now put a = 6 and d = 4 and Tn = 174 in Tn = a+(n-1)d :-

⟹ Tn = a+(n-1)d

⟹ 174 = 6 +(n-1)4

⟹ 174 = 6 +4n -4

⟹ 174 = 2+4n

⟹ 174-2 = 4n

⟹ 172 = 4n

⟹ 172 /4 = n

or

⟹ n= 172 /4

⟹ n= 172 /4

⟹ n= 43

Answer :

Number of terms of given AP = 43

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Learn more :-

1. Tn = a+(n-1)d

2. Sn = n/2[2a+(n-1)d]

3. Sn = n/2(a+l)

4. Common difference = b - a

where :-

• a = first term
• b = second terms
• d = common difference
• Tn = nth term
• l = last term

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