Let the first three terms and , with , of a G.P. be respectively the and terms of an A.P. If the term of the G.P. is the term of the A.P., then is equal to:

Question

Let the first three terms  and , with , of a G.P. be respectively the  and  terms of an A.P. If the  term of the G.P. is the  term of the A.P., then  is equal to:

Canvas Classes · Accepted Answer

🧠 Reading the Question — Express  Via A.P., Then Apply G.P. Condition

Read this slowly. Three numbers  are in G.P. AND they are the 7th, 8th, 13th terms of an A.P. with first term  and common difference .

From the A.P.: , , .

So  (since ) and .

G.P. condition: , so .

Expand: .

gives , violating . So .

Then . G.P. is  with common ratio .

5th G.P. term: .

Find  such that this equals the -th A.P. term. From : . Then .

The habit: two progressions linked by overlapping terms → set up both

More questions from this chapter

More questions from this chapter